Chemotherapy With or Without Trastuzumab After Surgery in Treating Women With Invasive Breast Cancer

Inclusion Criteria: * Patients should have a life expectancy of at least 10 years, excluding their diagnosis of breast cancer; (comorbid conditions should be taken into consideration, but not the diagnosis of breast cancer) * Women of reproductive potential must agree to use an effective non-hormonal method of contraception (for example condoms, some intrauterine devices, diaphragms, tubal ligation, vasectomized partner, or abstinence) during therapy and for at least 6 months (Arm 1 patients) and for at least 7 months (Arm 2 patients) after the last dose of study therapy (chemotherapy or trastuzumab) * Submission of tumor samples from the breast surgery is required for all patients; therefore, the local pathology department policy regarding release of tumor samples must be considered in the screening process; patients whose tumor samples are located in a pathology department that by policy will not submit any samples for research purposes should not be approached for participation in the B-47 trial * The patient must have signed and dated an Institutional Review Board (IRB)-approved consent form that conforms to federal and institutional guidelines * Eastern Cooperation Oncology Group (ECOG) performance status of 0 or 1 * The tumor must be unilateral invasive adenocarcinoma of the breast on histologic examination * All of the following staging criteria (according to the 7th edition of the American Joint Committee on Cancer \[AJCC\] Cancer Staging Manual) must be met: * By pathologic evaluation, primary tumor must be pT1-3 * By pathologic evaluation, ipsilateral nodes must be pN0, pN1 (pN1mi, pN1a, pN1b, pN1c), pN2a, pN2b, pN3a, or pN3b * If pN0, one of the following criteria must be met: * pT2 and estrogen receptor (ER) negative and progesterone receptor (PgR) negative; or * pT2 and ER positive (PgR status may be positive or negative) and either grade 3 histology or Oncotype DX Recurrence Score of \>= 25; or * pT3 regardless of hormone receptor status, histologic grade, and Oncotype DX Recurrence Score * HER2 status of the primary tumor must be evaluated prior to randomization; all testing performed must indicate that the tumor is HER2-low as defined below * IHC must be performed and the IHC staining results must indicate a score of 1+ (in situ hybridization \[ISH\] testing is not required) or 2+ (ISH must also be performed and must indicate that the tumor is HER2-low as described below) * If ISH testing is performed, test results must be as follows and IHC must be 1+ or 2+: the ratio of HER2 to chromosome enumeration probe 17 (CEP17) must be \< 2.0 or, if a ratio was not performed, the HER2 gene copy number must be \< 4 per nucleus * Note: If the IHC staining intensity is reported as a range, e.g., 0 to 1+ or 1+ to 2+, the higher intensity score in the range should be used to determine eligibility * The patient must have undergone either a total mastectomy or breast-conserving surgery (lumpectomy); (patients who have had a nipple-sparing mastectomy are eligible) * For patients who undergo lumpectomy, the margins of the resected specimen must be histologically free of invasive tumor and ductal carcinoma in situ (DCIS) as determined by the local pathologist; if pathologic examination demonstrates tumor at the line of resection, additional operative procedures may be performed to obtain clear margins; if tumor is still present at the resected margin after re-excision(s), the patient must undergo total mastectomy to be eligible; (patients with margins positive for lobular carcinoma in situ \[LCIS\] are eligible without additional resection) * For patients who undergo mastectomy, margins must be free of gross residual tumor; (patients with microscopic positive margins are eligible as long as post-mastectomy radiation therapy \[RT\] of the chest wall will be administered) * The patient must have completed one of the procedures for evaluation of pathologic nodal status listed below: * Sentinel lymphadenectomy alone: * If pathologic nodal staging based on sentinel lymphadenectomy is pN0 or pN1b * If pathologic nodal staging based on sentinel lymphadenectomy is pN1mi or pN1a, the primary tumor must be T1 or T2 by pathologic evaluation and the nodal involvement must be limited to 1 or 2 positive nodes * Sentinel lymphadenectomy followed by removal of additional non-sentinel lymph nodes if the sentinel node (SN) is positive; or * Axillary lymphadenectomy with or without SN isolation procedures * The interval between the last surgery for breast cancer (treatment or staging) and randomization must be no more than 84 days * The patient must have ER analysis performed on the primary tumor prior to randomization; if ER analysis is negative, then PgR analysis must also be performed (either the core biopsy or surgical resection specimen can be used for ER/PgR testing); patients with a primary tumor that is hormone receptor-positive or receptor-negative are eligible * Absolute neutrophil count (ANC) must be \>= 1,200/mm\^3 * Platelet count must be \>= 100,000/mm\^3 * Hemoglobin must be \>= 10 g/dL * Total bilirubin must be =\< upper limit of normal (ULN) for the lab unless the patient has a bilirubin elevation \> ULN to 1.5 x ULN due to Gilbert disease or similar syndrome involving slow conjugation of bilirubin * Alkaline phosphatase must be =\< 2.5 x ULN for the lab * Aspartate aminotransferase (AST) must be =\< 1.5 x ULN for the lab (if alanine aminotransferase \[ALT\] is performed instead of AST \[per institution's standard practice\], the alanine aminotransferase \[ALT\] value must be =\< 1.5 x ULN; if both were performed, the AST must be =\< 1.5 x ULN) * Alkaline phosphatase and AST may not both be \> the ULN * Patients with AST or alkaline phosphatase \> ULN are eligible for inclusion in the study if liver imaging (computed tomography \[CT\], magnetic resonance imaging \[MRI\], positron emission tomography \[PET\]-CT, or PET scan) performed within 90 days prior to randomization does not demonstrate metastatic disease and the above requirements are met * Patients with alkaline phosphatase that is \> ULN but =\< 2.5 x ULN or unexplained bone pain are eligible for inclusion in the study if a bone scan, PET-CT scan, or PET scan performed within 90 days prior to randomization does not demonstrate metastatic disease * The most recent postoperative serum creatinine performed within 6 weeks prior to randomization must be =\< ULN for the lab * Left ventricular ejection fraction (LVEF) assessment must be performed within 90 days prior to randomization; LVEF assessment performed by 2-dimensional (D) echocardiogram is preferred, however, multi-gated acquisition (MUGA) scan maybe substituted based on institutional preferences * For patients who will receive the TC chemotherapy regimen, the LVEF must be \>= 50% regardless of the cardiac imaging facility's lower limit of normal * For patients who will receive the AC--\>WP chemotherapy regimen, the LVEF must be \>= 55% regardless of the cardiac imaging facility's lower limit of normal * NOTE: Since the pre-entry LVEF serves as the baseline for comparing subsequent LVEF assessments, it is critical that this baseline study be an accurate assessment; if the baseline LVEF is \> 70%, the investigator is encouraged to have the accuracy of the initial LVEF result confirmed and repeat the test if the accuracy is uncertain Exclusion Criteria: * Primary tumor with any of the following HER2 testing results: * IHC staining intensity: * 0 on all evaluations of specimens * 3+ on evaluation of any specimen * ISH with a ratio of HER2 to CEP17 \>= 2.0 on evaluation of any specimen * ISH result indicating HER2 gene copy number \>= 4 per nucleus on evaluation of any specimen * T4 tumors including inflammatory breast cancer * Definitive clinical or radiologic evidence of metastatic disease * NOTE: Chest imaging (mandatory for all patients) and other imaging (if required) must have been performed within 90 days prior to randomization * Synchronous or previous contralateral invasive breast cancer (patients with synchronous and/or previous contralateral DCIS or LCIS are eligible) * Any previous history of ipsilateral invasive breast cancer or ipsilateral DCIS; (patients with synchronous or previous ipsilateral LCIS are eligible) * History of non-breast malignancies (except for in situ cancers treated only by local excision and basal cell and squamous cell carcinomas of the skin) within 5 years prior to randomization * Previous therapy with anthracyclines, taxanes, or trastuzumab for any malignancy * Chemotherapy or HER2-targeted therapy administered for the currently diagnosed breast cancer prior to randomization * Whole-breast RT prior to randomization or partial-breast RT that cannot be completed on or before the date of randomization * Continued endocrine therapy such as raloxifene or tamoxifen (or other selective estrogen receptor modulator \[SERM\]) or an aromatase inhibitor; patients are eligible if these medications are discontinued prior to randomization * Any continued use of sex hormonal therapy, e.g., birth control pills, ovarian hormone replacement therapy; patients are eligible if these medications are discontinued prior to randomization * Cardiac disease (history of and/or active disease) that would preclude the use of the drugs included in the treatment regimens; this includes but is not confined to: * Active cardiac disease: * Angina pectoris that requires the current use of anti-anginal medication * Ventricular arrhythmias except for benign premature ventricular contractions * Supraventricular and nodal arrhythmias requiring a pacemaker or not controlled with medication * Conduction abnormality requiring a pacemaker * Valvular disease with documented compromise in cardiac function * Symptomatic pericarditis * History of cardiac disease: * Myocardial infarction documented by elevated cardiac enzymes or persistent regional wall abnormalities on assessment of left ventricle (LV) function * History of documented congestive heart failure (CHF) * Documented cardiomyopathy * Hypertension defined according to the following ineligibility criteria: * For patients who will receive TC (regardless of the patient's age): uncontrolled hypertension defined as sustained systolic blood pressure (BP) \> 150 mm Hg or diastolic BP \> 90 mm Hg; (patients with initial BP elevations are eligible if initiation or adjustment of BP medication lowers pressure to meet entry criteria) * For patients \< 50 years old who will receive AC--\>WP: uncontrolled hypertension defined as sustained systolic BP \> 150 mm Hg or diastolic BP \> 90 mm Hg; patients with initial BP elevations are eligible if initiation or adjustment of BP medication lowers pressure to meet entry criteria * For patients \>= 50 years old who will receive AC--\>WP: * Uncontrolled hypertension defined as sustained systolic BP \> 150 mm Hg or diastolic BP \> 90 mm Hg * Controlled hypertension (systolic BP =\< 150 mm Hg and diastolic BP =\< 90 mmHg), if anti-hypertensive medication(s) are needed * NOTE: Patients who are not eligible based on the AC-WP regimen BP criteria but who meet the TC regimen BP criteria are eligible for B-47, if the intended chemotherapy regimen is changed to TC * Active hepatitis B or hepatitis C with abnormal liver function tests * Intrinsic lung disease resulting in dyspnea * Poorly controlled diabetes mellitus * Active infection or chronic infection requiring chronic suppressive antibiotics * Nervous system disorder (paresthesia, peripheral motor neuropathy, or peripheral sensory neuropathy) \>= grade 2, per the Common Terminology Criteria for Adverse Events (CTCAE) version (v)4.0 * Conditions that would prohibit administration of corticosteroids * Chronic daily treatment with corticosteroids with a dose of \>= 10 mg/day methylprednisol one equivalent (excluding inhaled steroids) * Known hypersensitivity to any of the study drugs or excipients, e.g., polysorbate 80 and Cremophor EL * Pregnancy or lactation at the time of study entry; (Note: pregnancy testing must be performed within 2 weeks prior to randomization according to institutional standards for women of childbearing potential) * Other non-malignant systemic disease that would preclude the patient from receiving study treatment or would prevent required follow-up * Psychiatric or addictive disorders or other conditions that, in the opinion of the investigator, would preclude the patient from meeting the study requirements * Use of any investigational product within 30 days prior to randomization