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ролд17
@ролд17
July 2022
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Разложите на множители :(2х+3у)^3+(3х-2у)^3
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IrkaShevko
Verified answer
A³ + b³ = (a + b)(a² - ab + b²)
(2x + 3y + 3x - 2y)((2x + 3y)² - (2x + 3y)(3x - 2y) + (3x - 2y)²) =
= (5x + y)(4x² + 9y² + 12xy - 6x² - 9xy + 4xy + 6y² + 9x² + 4y² - 12xy) =
= (5x + y)(7x² + 19y² - 5xy)
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Answers & Comments
Verified answer
A³ + b³ = (a + b)(a² - ab + b²)(2x + 3y + 3x - 2y)((2x + 3y)² - (2x + 3y)(3x - 2y) + (3x - 2y)²) =
= (5x + y)(4x² + 9y² + 12xy - 6x² - 9xy + 4xy + 6y² + 9x² + 4y² - 12xy) =
= (5x + y)(7x² + 19y² - 5xy)