Question

Write as a product:


x^3+x^2y–4y–4x


y^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)`

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)`