Chapter 13, Problem 1IR

To determine

The complete factor for the given expression $x^2+2xy+y^2$ .

Answer to Problem 1IR

  $\left(x+y\right)\left(x+y\right)$

Explanation of Solution

Given:

Given expression is $x^2+2xy+y^2$ .

Calculation:

Let us take the given expression, $x^2+2xy+y^2$ .

Which is in the form of $a^2+2ab+b^2$

We already know that, $a^2+2ab+b^2={\left(a+b\right)}^2$

So, write the given expression in the form of ${\left(a+b\right)}^2$ .

That is,

  $x^2+2xy+y^2={\left(x+y\right)}^2$

Now, we can write

  ${\left(x+y\right)}^2=\left(x+y\right)\left(x+y\right)$

Conclusion:

Therefore, the complete factor for $x^2+2xy+y^2$ is $\left(x+y\right)\left(x+y\right)$ .