Solve (x+1)² + (x+2)²: Sum of Squared Binomial Expressions

(x+1)2+(x+2)2= (x+1)^2+(x+2)^2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simply
00:07 We'll use the shortened multiplication formulas to open the parentheses
00:35 We'll calculate the multiplications and squares
00:41 We'll collect like terms
00:57 We'll factor out the common term from the parentheses
00:59 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

(x+1)2+(x+2)2= (x+1)^2+(x+2)^2=

2

Step-by-step solution

In order to solve the exercise, we will need to know the abbreviated multiplication formula:

In this exercise, we will use the formula twice:

(x+1)2=x2+2x+1 (x+1)^2=x^2+2x+1

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

Now, we add:

x2+2x+1+x2+4x+4=2x2+6x+5 x^2+2x+1+x^2+4x+4=2x^2+6x+5

x²+2x+1+x²+4x+4=
2x²+6x+5

Note that a common factor can be extracted from part of the digits: 2(x2+3x)+5 2(x^2+3x)+5

3

Final Answer

2(x2+3x)+5 2(x^2+3x)+5

Practice Quiz

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


\( (x+3)^2 \)

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