Chapter 8.4, Problem 7LC

To determine

To find: the rule should be used to find the product.

Answer to Problem 7LC

The rule of finding this product is:- square of a binomial.

Explanation of Solution

Given information:

Given product,

  $\left(7x+2\right)\left(7x+2\right)$

Calculation:

Consider the product $\left(7x+2\right)\left(7x+2\right)$

Here simplify this expression using the formula,

  ${\left(a+b\right)}^2=a^2+2ab+b^2$

And compare this formula with given expression,

  $\begin{array}{l}a=7x\\ b=2\end{array}$

Put the value of $a$ and $b$ in formula,

  $\begin{array}{c}{\left(7x+2\right)}^2={\left(7x\right)}^2+2\left(7x\right)\left(2\right)+{\left(2\right)}^2\\ =49x^2+28x+4\end{array}$

Since this expression is in the form of the square of a binomials.

That why it is solved using square of a binomial rule,

So,

The rule of finding this product is:- square of a binomial.