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Chapter 6: Problem 201

Multiply. $$5 q^{3}\left(q^{2}-2 q+6\right)$$

Short Answer

Expert verified
5q^5 - 10q^4 + 30q^3.

Step by step solution

01

- Distribute the First Term

Multiply the first term inside the parentheses, which is \(q^2\), by \(5q^3\). The resulting term will be \((5q^3 \times q^2) = 5q^{5}\).
02

- Distribute the Second Term

Multiply the second term inside the parentheses, which is \(-2q\), by \(5q^3\). The resulting term will be \((5q^3 \times -2q) = -10q^{4}\).
03

- Distribute the Third Term

Multiply the third term inside the parentheses, which is \(6\), by \(5q^3\). The resulting term will be \((5q^3 \times 6) = 30q^{3}\).
04

- Combine the Terms

Combine all the resulting terms from steps 1, 2, and 3. The final expression is \(5q^5 - 10q^4 + 30q^3\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distributive property
When multiplying polynomials, a key concept used is the distributive property. This property allows us to distribute or
combining like terms
After distributing all the terms, we may need to combine like terms.
exponents
Understanding exponents is important when multiplying polynomials. When you multiply terms with the same base,

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Most popular questions from this chapter

Divide each polynomial by the binomial. $$\left(6 m^{2}-19 m-20\right) \div(m-4)$$

Divide each polynomial by the monomial. $$\frac{52 p^{5} q^{4}+36 p^{4} q^{3}-64 p^{3} q^{2}}{4 p^{2} q}$$

Simplify. (a) \(2 \cdot 5^{-1}\) (b) \((2 \cdot 5)^{-1}\)

Divide each polynomial by the monomial. $$\frac{18 y^{2}-12 y}{-6}$$

Mixed Practice $$\frac{27 a^{7}}{3 a^{3}}+\frac{54 a^{9}}{9 a^{5}}$$
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