Question

Multiply. $$ 3 a^{2} b\left(a b^{2}+6 a b-13 b+7\right) $$

   Multiply.
$$
3 a^{2} b\left(a b^{2}+6 a b-13 b+7\right)
$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 6, Problem 15

Instant Answer

Solved by Expert Kristen Marte

02/19/2021

Step 1

This gives us: $$ 3a^{2}b \cdot ab^{2} + 3a^{2}b \cdot 6ab - 3a^{2}b \cdot 13b + 3a^{2}b \cdot 7 $$ Show more…

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Multiply. $$ 3 a^{2} b\left(a b^{2}+6 a b-13 b+7\right) $$

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Key Concepts

Distributive Property

The distributive property is a core principle in algebra which states that a term multiplied by a sum of terms can be distributed across each term in the sum. This property allows for the expansion of expressions by multiplying the external monomial by each term within the parentheses, ensuring that no term is left out during multiplication.

Monomial Multiplication

Monomial multiplication involves multiplying a single term (a monomial) by another term or a set of terms in a polynomial. In this process, numerical coefficients are multiplied together and exponents of like variables are added according to the laws of exponents, which is fundamental to correctly expanding and simplifying algebraic expressions.

Laws of Exponents

The laws of exponents are a set of rules that simplify the process of multiplying and dividing exponential expressions. These rules, such as adding the exponents when multiplying like bases, are essential during the expansion of polynomial expressions, ensuring that the powers of variables are correctly combined in the result.

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