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

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

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

2

Step-by-step solution

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

(x+y)2=x2+2xy+y2 (x+y)^2=x^2+2xy+y^2

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

(x+3)2=x2+6x+9 (x+3)^2=x^2+6x+9

(x+2)2=x2+4x+4 (x+2)^2=x^2+4x+4

We then reinsert them back into the formula as follows:

2(x2+6x+9)+3(x2+4x+4)= 2(x^2+6x+9)+3(x^2+4x+4)=

2x2+12x+18+3x2+12x+12= 2x^2+12x+18+3x^2+12x+12=

5x2+24x+30 5x^2+24x+30

3

Final Answer

5x2+24x+30 5x^2+24x+30

Practice Quiz

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Choose the expression that has the same value as the following:


\( (x+3)^2 \)

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