Question

Разложить на множители Решите хотябы 1 1 ) ( 2x + y )³ - x³2) 8p³ - ( p + 1 )³

Answer 1

$a^3-b^3=(a-b)(a^2+ab+b^2)$


1) $(2x+y)^3-x^3=(2x+y-x)(4x^2+2xy+y^2)= \\ \\ =(x+y)(4x^2+2xy+y^2)$

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2) $8p^3-(p+1)^3=(2p)^3-(p+1)^3= \\ \\ =(2p-(p+1))(4p^2+2p(p+1)+(p+1)^2)= \\ \\ =(p+1)(4p^2+2p^2+2p+p^2+2p+1)= \\ \\ =(p+1)(7p^2+4p+1)$