Solve (x-2)² + (x-3)² = : Expanding Square Binomials

Question

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

00:00 Simply

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

00:11 X is the A in the formula

00:17 And 2 is the B in the formula

00:30 We'll use the same formula where X is A and 3 is B

00:40 Let's solve the multiplications

00:53 Let's group the factors

01:06 And this is the solution to the question

In order to solve the question, we need to know one of the shortcut multiplication formulas:

$(x−y)^2=x^2−2xy+y^2$

We apply the formula twice:

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

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

Now we add the two together:

$x^2-4x+4+x^2-6x+9=$

$2 x^2-10x+13$

$2x^2-10x+13$