Expand and Simplify: 2(x+3)² + 3(x+2)² Expression

Question

$2(x+3)^2+3(x+2)^2=$

00:00 Simply

00:03 We'll use the shortened multiplication formulas to open the parentheses

00:38 We'll solve the squares and products

00:59 We'll properly open parentheses and multiply by each factor

01:29 We'll collect like terms

01:44 And this is the solution to the question

In order to solve the exercise, remember the abbreviated multiplication formulas:

$(x+y)^2=x^2+2xy+y^2$

Let's start by using the property in both cases:

$(x+3)^2=x^2+6x+9$

$(x+2)^2=x^2+4x+4$

We then reinsert them back into the formula as follows:

$2(x^2+6x+9)+3(x^2+4x+4)=$

$2x^2+12x+18+3x^2+12x+12=$

$5x^2+24x+30$

$5x^2+24x+30$