Q. 218 - Intermediate Algebra

Question

In the following exercises, factor completely.
$36y^2+12y+1$

Step-by-Step Solution

Answer

The factored form of the given expression is ${(6y+1)}^2$.

Step 1. Given information.

The given expression is:

$36y^2+12y+1$

Step 2. Determine the factored form.

The given expression can be written as:
$\begin{array}{rcl}36y^2+12y+1& =& 6^2{y}^2+2\left(6y\right)\left(1\right)+1^2\\ & =& {\left(6y\right)}^2+2\left(6y\right)\left(1\right)+1^2\\ & =& {(6y+1)}^2 [\because (a+b{)}^2=a^2+2ab+b^2]\end{array}$

Step 3. Conclusion.

The factored form of the given expression is ${(6y+1)}^2$.