Chapter 14, Problem 37SGR

To determine

To calculate: The value of $\left(5a-2\right)\left(5a-2\right)$ by multiplication model.

Answer to Problem 37SGR

The requiredmultiplication of the expression $\left(5a-2\right)\left(5a-2\right)$ is $25a^2-20a+4$ .

Explanation of Solution

Given Information:

The expression is $\left(5a-2\right)\left(5a-2\right)$ .

Formula Used:

The distributive formula is:

  $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)$

Calculation:

The given expression is $\left(5a-2\right)\left(5a-2\right)$ .

Find the multiplication of the expression $\left(5a-2\right)\left(5a-2\right)$ .

Use the distributive formula $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)$

  $\left(5a-2\right)\left(5a-2\right)=\left(5a\right)\left(5a-2\right)+\left(-2\right)\left(5a-2\right)$

Use again distributiveformula $\left(a+b\right)\left(c+d\right)=a\left(c+d\right)+b\left(c+d\right)$

  $\left(5a\right)\left(5a-2\right)+\left(-2\right)\left(5a-2\right)=\left(5a\right)\left(5a\right)+\left(5a\right)\left(-2\right)+\left(-2\right)\left(5a\right)+\left(-2\right)\times \left(-2\right)$

Use multiplication on the right hand side and simplify.

  $\begin{array}{c}\left(5a\right)\left(5a-2\right)+\left(-2\right)\left(5a-2\right)=\left(5a\right)\left(5a\right)+\left(5a\right)\left(-2\right)+\left(-2\right)\left(5a\right)+\left(-2\right)\times \left(-2\right)\\ =25a^2-10a-10a+4\\ =25a^2-20a+4\end{array}$

Hence, the required multiplication of the expression $\left(5a-2\right)\left(5a-2\right)$ is $25a^2-20a+4$ .