Polynomial Inequalities | MathHelp.com - Free Educational videos for Students in K-12 | Lumos Learning

## Polynomial Inequalities | MathHelp.com - Free Educational videos for Students in k-12

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In this example, weâre asked to factor 125p cubed + 1. Notice that 125p cubed is a perfect cube, because 125 is 5 times 5 times 5, or 5 cubed, and 1 is a perfect cube, because 1 is 1 times 1 times 1, or 1 cubed. So we have the sum of two cubes. To factor the sum of two cubes, we use the following formula: a cubed + b cubed can be factored as parentheses a + b times parentheses a squared â ab + b squared. And in this problem, since a cubed is represented by 125p cubed, the value of a is 5p, and since b cubed is represented by 1, the value of b is 1. Notice that the value of a, 5p, has both a coefficient and a variable, so we need to use parentheses around the 5p when we plug it into the formula, in order to keep the 5 and the p together. And letâs go ahead and use parentheses around our x as well, in order to be consistent. So we have bracket parentheses 5p + parentheses 1 closed bracket times bracket parentheses 5p squared + parentheses 5p times parentheses 1 + parentheses 1 squared closed bracket. Notice that we change the parentheses in the formula to brackets so that weâre not dealing with too many sets of parentheses. Next, simplifying inside of the second set of brackets, parentheses 5p squared is 5p times 5p, or 25p squared, 5p times 1 is 5p, so we have â 5p, and parentheses 1 squared is 1, so we have plus 1. And changing the brackets back to parentheses, we have parentheses 5p + 1 times parentheses 25p squared â 5p + 1, which is our final answer.

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