Question

In the following exercises, factor each trinomial of the form $x^2+bxy+c{y}^2$

$m^2-12mn+20n^2$

Short answer

The factorization of$m^2-12mn+20n^2$is$(m-2n)(m-10n)$

Step-by-step solution

Step 1. Given information

Given expression is$m^2-12mn+20n^2$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

The factors of 20	Sum of factors
5, 4	5 + 4 = 9
10, 2	10 + 2 = 12
-5, -4	-5 + (-4) = -9
-10, -2	-10 + (-2) = -12

Step 3. Factorization

Use $-2$and $-10$as the last terms of the trinomials.

$m^2-12mn+20n^2=(m-2n)(m-10n)$

Step 4. Check

$$\begin{gathered} (m-2n)(m-10n)=m^2-2mn-10mn+20n^2 \\ =m^2-12mn+20n^2 \end{gathered}$$