Question

How do you factor `2( a+b) ^2 + (a+b) - 21`?

Answer 1

`(2a+2b+7)(a+b-3)`

Explanation:

`"make the substitution "u=a+b" then"`

`2u^2+u-21larrcolor(blue)"is the expression to be factored"`

`"the product of - 42 which sums to + 1 is + 7 and - 6"`

`rArr2u^2-6u+7u-21`

`=color(red)(2u)(u-3)color(red)(+7)(u-3)`

`=(u-3)(color(red)(2u+7))`

`"changing u back to a + b"`

`=(a+b-3)(2a+2b+7)`

`rArr2(a+b)^2+(a+b)-21`

`=(a+b-3)(2a+2b+7)`