Question

(x+2y)(x²-2xy +4y²)by using suitable identity​

Answer 1

By using identity,

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

So ATQ,

$-> (x + 2y)( {x}^{2} - 2xy + 4 {y}^{2} ) \\ \\ -> x( {x}^{2} - 2xy + 4 {y}^{2} ) + 2y({x}^{2} - 2xy + 4 {y}^{2} ) \\ \\ -> {x}^{3} - 2 {x}^{2} y + 4 {y}^{2} x + 2y {x}^{2} - 4x {y}^{2} + 8 {y}^{3} \\ \\ -> {x}^{3} - 2y {x}^{2} + 2y {x}^{2} + 4 {y}^{2} x - 4x {y}^{2} + 8 {y}^{3} \\ \\ now \\ \\ - 2 {x}^{2} y + 2y {x}^{2} get \: cancelled \: and \: + 4 {y}^{2} x - 4 {y}^{2} x \: are \: also \: get \: cancelled \: so \: our \: answer \: is \: \\ \\ </h3><h2>= {x}^{3} + {(2y)}^{3}$

Answer 2

Hi friend!!

Given,

(x+2y)(x²-2xy+4y²)

=(x+2y)(x²-(x)(2y)+(2y)²)

We know that (a+b)(a²+b²-ab)=a³+b³

=x³+(2y)³

=x³+8y³

I hope this will help you ;)