Video: Expanding a Difference of Two Squares

Expand the product (π‘₯ + 1)(π‘₯ βˆ’ 1).

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Video Transcript

Expand the product π‘₯ plus one multiplied by π‘₯ minus one.

The word product means multiply. In order to expand the product π‘₯ plus one multiplied by π‘₯ 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, π‘₯ multiplied by π‘₯ gives us π‘₯ squared. Multiplying the outside terms, π‘₯ multiplied by negative one gives us negative one π‘₯, or minus one π‘₯. Multiplying the inside terms, positive one multiplied by π‘₯ gives us positive one π‘₯, or plus π‘₯. And finally, multiplying the last terms, positive one multiplied by negative one gives us negative one. This leaves us with the expression π‘₯ squared minus π‘₯ plus π‘₯ minus one. As negative π‘₯ plus π‘₯ equals zero, we are able to simplify this equation, leaving us with π‘₯ squared minus one.

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

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