(a+b)⁴-(a-b)⁴Представьте в виде произведения. Created by camikilla. algebra-ru

(a+b)⁴-(a-b)⁴Представьте в виде произведения...

June 2021 1 18 Report

(a+b)⁴-(a-b)⁴
Представьте в виде произведения

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aliyas1
${(a + b})^{4} - {(a - b})^{4} = \\ = ({(a + b})^{2} - {(a - b})^{2})({(a + b})^{2} + {(a - b})^{2}) = \\ = ({a}^{2} + 2ab + {b}^{2} - {a}^{2} + 2ab - {b}^{2} ) \times \\ \times ({a}^{2} + 2ab + {b}^{2} + {a}^{2} - 2ab + {b}^{2}) = \\ = 4ab(2 {a}^{2} + 2 {b}^{2} ) = \\ = 8ab({a}^{2} + {b}^{2})$

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