Question

In your own words, describe two binomials that, when multiplied, results in the difference of two squares. Give examples and show the product.

Answer 1

In your own words, describe two binomials that, when multiplied, results in the difference of two squares.

Let the binomials be

`(x+a)\text{ and }(x-a)`

Where the first term is x and the second term is a

Multiplying the binomials

`\begin{gathered} (x+a)(x-a)=(x)^2-(a)^2=x^2-a^2 \\ (x+a)(x-a)=x^2-a^2 \end{gathered}`

Hence, when multiplied, the result is the difference of two squares.

Assuming the binomials, for example are

`(2x+2)\text{ and }(2x-2)`

Their product will give

`\begin{gathered} (2x+2)(2x-2)=(2x)^2-(2)^2=4x^2-4 \\ (2x+2)(2x-2)=4x^2-4 \end{gathered}`

Hence, the product is

`4x^2-4`