Question

8x^3+12x^2y+6xy^2-7y^3

Answer 1

$\textbf{Given:}$

$8x^3+12x^2y+6xy^2-7y^3$

$\textbf{To find:}$

$\text{Factors of}\;8x^3+12x^2y+6xy^2-7y^3$

$\text{Consider,}$

$8x^3+12x^2y+6xy^2-7y^3$

$\text{Add and subtract y^3 }$

$=[8x^3+12x^2y+6xy^2+y^3]-8y^3$

$=[(2x)^3+3(2x)^2y+3(2x)y^2+y^3]-8y^3$

$\text{Using the identity}$

$\bf\,a^3+3a^2b+ab^2+b^3=(a+b)^3$

$=(2x+y)^3-(2y)^3$

$\text{Using the identity}$

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

$=(2x+y-2y)[(2x+y)^2+(2x+y)2y+(2y)^2]$

$=(2x-y)[4x^2+y^2+4xy+4xy+2y^2+4y^2]$

$=(2x-y)(4x^2+8xy+7y^2)$

$\therefore\bf\;8x^3+12x^2y+6xy^2-7y^3=(2x-y)(4x^2+8xy+7y^2)$

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Answer 2

Answer:

Step-by-step explanation: