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Chapter 5: Problem 36

Find each product. $$2 a b^{2}\left(20 a^{2} b^{3}+11 a b\right)$$

Short Answer

Expert verified
The simplified product is \(40 a^{3} b^{5} + 22 a^{2} b^{3}\)

Step by step solution

01

Understanding the Distributive Law

The Distributive Property states that when multiplying a term by terms inside parentheses (which may be a sum or difference), apply the multiplication to each term inside the parentheses one at a time. Here, the expression can be written as \(2 a b^{2}\) * \(20 a^{2} b^{3}\) + \(2 a b^{2}\) * \(11 a b\) .
02

Multiplying the Terms

Multiplication of polynomials implies multiplying the coefficients (numerical factors) and adding the exponents of any matching bases (variable factors). This results in \(40 a^{3} b^{5}\) + \(22 a^{2} b^{3}\).
03

Simplification of the expression

The expression is already simplified as there are no like terms (terms that have the same variable and exponent) to combine. Hence the final result is: \(40 a^{3} b^{5} + 22 a^{2} b^{3}\)

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Most popular questions from this chapter

Perform the indicated computations. Express answers in scientific notation. $$\frac{\left(1.2 \times 10^{6}\right)\left(8.7 \times 10^{-2}\right)}{\left(2.9 \times 10^{6}\right)\left(3 \times 10^{-3}\right)}$$

Explain how to find any nonzero number to the 0 power.

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