Question

How to factorise:
9 (x+y)^3-16 (x+y)

Answer 1

GIVEN :

How to factorise :  $9(x+y)^3-16(x+y)$

TO FIND :

The factors of the given expression $9(x+y)^3-16(x+y)$

SOLUTION :

Given that the expression is $9(x+y)^3-16(x+y)$  

Now we have to factorise the given expression as below :

$9(x+y)^3-16(x+y)$

By using the algebraic identity :

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

$=9(x+y)(x+y)^2-16(x+y)$

Taking the common factor (x+y) outside,

$=[9(x+y)^2-16](x+y)$

$=[3^2(x+y)^2-4^2](x+y)$

By using the power rule of exponents property :

$a^mb^m=(ab)^m$

$=[(3(x+y))^2-4^2](x+y)$

By using the algebraic identity :

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

$=[3(x+y)+4][3(x+y)-4](x+y)$ ( here a=3(x+y) and b=4 )

By using the distributive property :

a(x+y)=ax+ay

$=(3x+3y+4)(3x+3y-4)(x+y)$

⇒ $9(x+y)^3-16(x+y)=(3x+3y+4)(3x+3y-4)(x+y)$

∴ the factors for the given expression  $9(x+y)^3-16(x+y)$ is (3x+3y+4), (3x+3y-4) and (x+y)

Answer 2

Answer:

THIS IS THE CORRECT ANSWER