Question

Which of the following represents the factorization of the binomial below?49x2-81y2Out of these 4 possible optionsA. (7x+y)(x-9y)B. (7x+9y)(7x-9y)C. (7x-9y)(7x-9y)D. (7x+9y)(7x+9y)

Answer 1

Option B

`\begin{equation*} \left(7x+9y\right)\left(7x-9y\right) \end{equation*}`

Step-by-step explanation

Given;

`49x^2-81y^2`

Factor out ;

`\begin{gathered} 49x^2=(7x)^2 \\ 81y^2=(9y)^2 \\ \left(7x\right)^2-\left(9y\right)^2 \end{gathered}`

Now, we have;

`\left(7x\right)^2-\left(9y\right)^2`

Using difference of two squares;

`\begin{gathered} x^2-y^2=(x+y)(x-y) \\ (7x)^2-(9y)^2=\left(7x+9y\right)\left(7x-9y\right) \end{gathered}`