Q 286 - Intermediate Algebra

Question

Multiply the following. $$\begin{gathered} \left(p+3\right)\left(p+3\right) \\ \left(q+6\right)\left(q+6\right) \\ \left(r+1\right)\left(r+1\right) \end{gathered}$$

Explain the pattern that you see in your answers.

Step-by-Step Solution

Answer

The product is  $$\begin{gathered} p^2+6p+9 \\ {q}^2+12q+36 \\ {r}^2+2r+1 \end{gathered}$$

The pattern seen in the answers is a Binomial square pattern.

Step 1. Given information

$$\begin{gathered} \left(p+3\right)\left(p+3\right) \\ \left(q+6\right)\left(q+6\right) \\ \left(r+1\right)\left(r+1\right) \end{gathered}$$

Step 2. Find the product

To square a binomial, square the first term, square the last term, and double their product.

$$\begin{gathered} {\left(p+3\right)}^2 \\ {\left(q+6\right)}^2 \\ {\left(r+1\right)}^2 \end{gathered}$$

Apply the perfect square formula

$$\begin{gathered} p^2+6p+9 \\ {q}^2+12q+36 \\ {r}^2+2r+1 \end{gathered}$$

The pattern seen in the answers is a binomial square pattern.