Chapter 8.7, Problem 20PPE

To determine

The solution of the given expression.

Answer to Problem 20PPE

The factor of expression $49g^2-84g+36$ is $\left(7g-6\right)\left(7g-6\right)$

Explanation of Solution

Given information:

The expression $49g^2-84g+36$

Concept and Formula Used:

The property ${\left(a-b\right)}^2=a^2-2ab+b^2$

Calculation:

The given expression is $49g^2-84g+36$

Write the first and last term of the expression as squares and middle term in the form of 2ab

  $49g^2-84g+36={\left(7g\right)}^2-2\times 7g\times 6+{\left(6\right)}^2$

Using the property ${\left(a-b\right)}^2=a^2-2ab+b^2$

Therefore

  $\begin{array}{l}49g^2-84g+36={\left(7g-6\right)}^2\\ 49g^2-84g+36=\left(7g-6\right)\left(7g-6\right)\end{array}$

Conclusion:

The factor of expression $49g^2-84g+36$ is $\left(7g-6\right)\left(7g-6\right)$