Q.225. - Intermediate Algebra

Question

Solve the square using the binomial squares pattern.

${\left(5u^2+9\right)}^2$

Step-by-Step Solution

Answer

The solution is $25u^4+90u^2+81$.

Step 1. Given information.

The given expression is ${\left(5u^2+9\right)}^2$.

Step 2. Simplify the given expression by using the binomial squares pattern a + b 2 = a 2 + 2 a b + b 2 .

Solve it as follows:

$$\begin{gathered} {\left(5u^2+9\right)}^2={\left(5u^2\right)}^2+2\times 5u^2\times 9+{\left(9\right)}^2 \\ \Rightarrow 25u^4+90u^2+81 \end{gathered}$$

Step 3. Binomial squares expression.

Hence, the binomial squares pattern are $25u^4+90u^2+81$.