Question

Write as a product:x^3+x^2y–4y–4xy^2(2y–5)–8y+20

Answer 1

Expression as product is :

x^3+x^2y–4y–4x  = $(x-2)(x+2)(x+y)$

y^2(2y–5)–8y+20 = $(y-2)(y+2)(2y-5)$

Step-by-step explanation:

Here we need to write , following expression as product:

x^3+x^2y–4y–4x

⇒ $x^3+x^2y-4y-4x$

 ⇒ $x^2(x+y)-4y-4x$

 ⇒ $x^2(x+y)-4(y+x)$

 ⇒ $(x^2-4)(x+y)$

 ⇒ $(x-2)(x+2)(x+y)$

y^2(2y–5)–8y+20

⇒ $y^2(2y-5)-8y+20$

 ⇒  $y^2(2y-5)-4(2)y+4(5)$

 ⇒  $y^2(2y-5)-4(2y-5)$

 ⇒   $(y^2-4)(2y-5)$

 ⇒   $(y-2)(y+2)(2y-5)$