Chapter 0.3, Problem 16E

To determine

To evaluate: the factors of polynomial.

Answer to Problem 16E

The factor of polynomial $x^2+4xy+4y^2$ is $\left(x+2y\right)\left(x+2y\right)$ .

Explanation of Solution

Given information :

Polynomial is given as $x^2+4xy+4y^2$

Factorizing the given polynomial,

  $\begin{array}{c}{x}^2+4xy+4y^2=x^2+2xy+2xy+4y^2\\ x^2+2xy+2xy+4y^2=x\left(x+2y\right)+2y\left(x+2y\right)\\ x\left(x+2y\right)+2y\left(x+2y\right)=\left(x+2y\right)\left(x+2y\right)\end{array}$

So,

After factorizing $\left(x+2y\right)\left(x+2y\right)$ .