Q 6.46TI. - Intermediate Algebra

Question

Factor: $9y^2+24y+16$.

Step-by-Step Solution

Answer

Factors of $9y^2+24y+16$ is ${\left(3y+4\right)}^2$, that is $\left(3y+4\right)\left(3y+4\right)$.

Step 1. Given information.

Given an expression $9y^2+24y+16$.

Step 2. Find if first and last term are perfect squares or not.

First term is $9y^2$ which can be expressed as ${\left(3y\right)}^2$.

Last term is 16 which can be expressed as $4^2$.

Consider $a=3y$ and $b=4$.

So, both first and last term are a perfect square.

Step 3. Check if the middle term is of the form ± 2 a b .

Here, middle term is $24y$ which can be expressed as $2\times 3y\times 4$.

It can be seen that middle term is of the form $2ab$.

Step 4. Write the square of the binomial.

So, $9y^2+24y+16$ is a perfect square trinomial of the form .

Note that .

Therefore, $9y^2+24y+16={\left(3y+4\right)}^2$.

Step 5. Check by multiplying.

Verification can be obtained as follows.

$\begin{array}{rcl}{\left(3y+4\right)}^2& =& {\left(3y\right)}^2+2\times 3y\times 4+4^2\\ & =& 9y^2+24y+16\end{array}$