Question

2(x+2y)^2 + 3(x+2y) +1​

Answer 1

Answer:

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

Step-by-step 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.

$2\times1=2$

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