Question

Please help me with this problem trying to help my son to understand.Factor.9x^2−49y^2 Enter your answer in the box.

Answer 1

This binomial can be factored as a difference of two squares. Taking the square root of each term, we get:

`\begin{gathered} a^2=9x^2 \\ a=\sqrt[]{9x^2} \\ a=\sqrt[]{9}\sqrt[]{x^2} \\ a=3x \end{gathered}`
`\begin{gathered} b^2=49y^2 \\ b=\sqrt[]{49y^2} \\ b=\sqrt[]{49}\sqrt[]{y^2} \\ b=7y \end{gathered}`

Difference of two squares formula

`a^2-b^2=(a+b)(a-b)`

Substituting with the values of a and b found, we get:

`9x^2-49y^2=(3x+7y)(3x-7y)`