Question

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

$x^2-2xy-80y^2$

Short answer

The factorization of$x^2-2xy+80y^2$is$(x+8y)(x-10y)$

Step-by-step solution

Step 1. Given information

Given expression is$x^2-2xy-80y^2$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

The factors of -80	Sum of factors
2, -40	2 + (-40) = -38
4, -20	4 + (-20) = -16
8, -10	8 + (-10) = -2
16, -5	16 + (-5) = 11

Step 3. Factorization

Use $8$and $-10$as the last terms of the trinomials.

$x^2-2xy-80y^2=(x+8y)(x-10y)$

Step 4. Check

$$\begin{gathered} (x+8y)(x-10y)=x^2+8xy-10xy-80y^2 \\ =x^2-2xy-80y^2 \end{gathered}$$