Question

2(x+2y)^2 + 3(x+2y) +1​

Answer 1

`3x+2y^2+2(x+y)+2y+1`

Explanation:

1) Split the second term in
`2{(x+2y)}^(2)+3(x+2y)+1` into two terms.

1 - Multiply the coefficient of the first term by the constant term.

`2*1=2`

2 - Ask: Which two numbers add up to 3 and multiply to 2?

2 and 1.

3 - Split
`3x+2y` as the sum of
`2(x+y)` and
`x+2y`.

`2x+2y^2+2(x+y)+x+2y+1`

2) Collect like terms.

`(2x+x)+2y^2+2(x+y)+2y+1`

3) Simplify.

`3x+2y^2+2(x+y)+2y+1`

Thank you,

Eddie