Question

In the following exercises, factor completely using the perfect square trinomials pattern.

$49x^2+28xy+4y^2$

Short answer

The factor of the trinomial is${\left(7x+2y\right)}^2$.

Step-by-step solution

Step 1. Given information.

Consider the given trinomial.

$49x^2+28xy+4y^2$

Step 2. Formula used 

$a^2+2ab+b^2={\left(a+b\right)}^2$

Step 3. Find the factor of perfect square trinomial.

The middle term of the trinomial is positive, so the binomial square will be of the form ${\left(a+b\right)}^2$.

$$\begin{gathered} {\left(7x\right)}^2+2·7x·2y+{\left(2y\right)}^2 \\ {\left(7x+2y\right)}^2 \end{gathered}$$