Find each product. See Example 5.4x² (3x³ + 2x² - 5x +1)

Question

Accepted Answer

Hello, everyone. We are going to perform the indicated operation to simplify the following polynomial expression. We are given nine U squared multiplied by the parentheses. U cubed plus four U squared minus seven U plus three. Our answer choices are a nine U raised to the fifth power plus 36 U raised to the fourth power plus 63 U cubed minus 27 U squared B nine U raised to the sixth power minus 36 U raised to the fourth power plus 63 U squared minus 27 C nine U raised to the fifth power 30 plus 36 U raised to the fourth power minus 63 U cubed plus 27 U squared D nine, U raised the sixth power plus 36. U raised the fourth power minus 63 U squared plus 27. I'm going to begin by rewriting our expression. So nine U squared multiplied by the parentheses. U cubed plus four U squared minus seven U plus three closed parentheses. So this is the distributive property. So I'm going to multiply nine U squared by each term inside our parentheses. So nine U squared multiplied by U cubed. This is like nine times one or nine multiplied by one which is nine, then U squared multiplied by U cubed. We keep the base and recall that we add our exponents when we multiply. So this will be nine U raised to the fifth power next nine U squared multiplied by four, U squared. Nine, multiplied by four is a positive 36 U squared multiplied by U squared. We keep the base of U. We'll add our exponents which will give us U raised to the fourth power. Next nine U squared multiplied by negative seven U nine multiplied by negative seven is negative 63 U squared multiplied by U raced to the first power. We'll keep the base of you. We'll add our exponents because if we don't see an exponent, it has a little one as an exponent. So two plus one is three. So this will be negative 63 U cubed. And our final multiplication will be nine U squared multiplied by three, nine, multiplied by three is a positive 27 U squared has nothing to multiply against to change it. So it stays U squared. So simplified, we are left with the expression nine U raised to the fifth power plus 36 U raised to the fourth power minus 63 U raised to the third power plus 27 U squared. And when we double check, that is answer choice C have a nice day.

Find each product. See Example 5.4x² (3x³ + 2x² - 5x +1)

Key Concepts

Polynomial Multiplication

Combining Like Terms

Degree of a Polynomial

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