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, weβre 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.
