Chapter 8.5, Problem 47P

Write the correct factored form for each expression.

$47\cdot x^2+5xy-14y^2$

To determine

To write : the correct factored form of given expression.

Answer to Problem 47P

  $\left(x+7y\right)\left(x-2y\right)$

Explanation of Solution

Given expression: $x^2+5xy-14y^2$

Calculation:

We will split the midle term into two terms whose sum is $5xy$ and product is $-14x^2{y}^2$ .

Therefore, by splitting the middle term , we get

  $\begin{array}{l}{x}^2+5xy-14y^2\\ =x^2+7xy-2xy-14y^2\\ =\left(x^2+7xy\right)+\left(-2xy-14y^2\right)\\ =x\left(x+7y\right)-2y\left(x+7y\right)\\ =\left(x+7y\right)\left(x-2y\right)\end{array}$

Thus, factored form of given expression is $\left(x+7y\right)\left(x-2y\right)$ .