Question Video: Expanding a Difference of Two Squares Mathematics • 9th Grade

Expand the product (𝑥 + 1)(𝑥 − 1).

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Video Transcript

Expand the product 𝑥 plus one multiplied by 𝑥 minus one.

The word product means multiply. In order to expand the product 𝑥 plus one multiplied by 𝑥 minus one, we’re going to use the FOIL method. The F stands for the first terms, the O for the outside ones, I for the inside, and the L for the last terms.

Multiplying the first terms, 𝑥 multiplied by 𝑥 gives us 𝑥 squared. Multiplying the outside terms, 𝑥 multiplied by negative one gives us negative one 𝑥, or minus one 𝑥. Multiplying the inside terms, positive one multiplied by 𝑥 gives us positive one 𝑥, or plus 𝑥. And finally, multiplying the last terms, positive one multiplied by negative one gives us negative one. This leaves us with the expression 𝑥 squared minus 𝑥 plus 𝑥 minus one. As negative 𝑥 plus 𝑥 equals zero, we are able to simplify this equation, leaving us with 𝑥 squared minus one.

Therefore, the expansion of the product 𝑥 plus one multiplied by 𝑥 minus one is equal to 𝑥 squared minus one. When the two brackets or parentheses are the same — with the exception of the sign in the middle, i.e., one is positive, and one is negative — this method is called the difference of two squares.

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