Question

8x^3+12x^2+6xy^2-7y^3.
solve​

Answer 1

Correct question :

$8 {x}^{3} +1 2 {x}^{2} \sf\mathbb\color{red} {y}\sf\mathbb\color{black} { + 6x {y}^{2} - 7 {y}^{3} }$

Step-by-step explanation:

Factors of 8x³ + 12x²y+6xy²-7y³

$\sf\mathbb\color{brown} {consider}$

8x³+12x²y+6xy²-7y³

Add and Subtract y³

= [ 8x³ + 12x ²y +6xy² + y³] - 8y³

= [(2x³ + 3(2x²y + 3 (2x) y² + y²] - 8y³

$\sf\mathbb\color{grey} {using \: the \: identity}$

a³ + 3a² b + ab² +b³ = ( a+b) ³

= (2x + y) ³-(2y)³

$\sf\mathbb\color{red} {using \: the \: identity}$

a³-b³ = ( a-b) (a²+ab+b²)

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

= (2x - y) (4x² +8xy + 7y²)

$\sf\mathbb\color{green} {∴ \: {8x}^{3} } + 12 {x}^{2} y + {6xy}^{2} - 7 {y}^{3} = (2x - y)(4 {x}^{2} + 8xy + {7y}^{2} )$