Question

How do you multiply polynomials `(x^2 + 2x - 1)(x^2 + 2x + 5)`?

Answer 1

`x^4+4x^3+6x^2+8x-5`

Explanation:

Just use a modified version of foil or a table

`x^2(x^2+2x+5)=x^4+2x^3+5x^2`

`2x(x^2+2x+5)=2x^3+2x^2+10x`

`-1(x^2+2x+5)=-x^2-2x-5`

Just add them all up

`x^4+2x^3+5x^2+2x^3+2x^2+10x-x^2-2x-5`

`x^4+color(red)(2x^3+2x^3)+color(blue)(5x^2+2x^2-x^2)+color(pink)(10x-2x)-5`

`x^4+color(red)(4x^3)+color(blue)(6x^2)+color(pink)(8x)-5`

Answer 2

`x^4+4x^3+8x^2+8x-5`

Explanation:

Given-

`(x^2+2x-1)(x^2+2x+5)`

`(x^2 xx x^2)+(2x xx x^2)-(1 xxx^2)+(x^2 xx 2x)+(2x xx 2x)-(1 xx 2x)+(x^2 xx5)+(2x xx5)-(1xx5)`

`x^4+2x^3-x^2+2x^3+4x^2-2x+5x^2+10x-5`

`x^4+2x^3+2x^3-x^2+4x^2+5x^2-2x+10x-5`

`x^4+4x^3+8x^2+8x-5`