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

Question

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

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

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

In this exercise, we will use the formula twice:

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

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

Now, we add:

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

x²+2x+1+x²+4x+4=
2x²+6x+5

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

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