Question

Find each product. $$-3 y\left(6-9 y+4 y^{2}\right)$$

   Find each product.
$$-3 y\left(6-9 y+4 y^{2}\right)$$

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 13, Problem 21

Instant Answer

Solved by Expert Julie Silva

05/20/2020

Step 1

This means we multiply $-3y$ by $6$, $-9y$, and $4y^2$ respectively. Show more…

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Find each product. $$-3 y\left(6-9 y+4 y^{2}\right)$$

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Key Concepts

Distributive Property

The distributive property is a fundamental principle in algebra which states that multiplying a sum or difference by a number is the same as doing each multiplication separately. This property is expressed as a(b + c) = ab + ac, and it allows for the simplification of expressions by distributing the multiplication over each term inside parentheses.

Monomial-Polynomial Multiplication

Multiplying a monomial by a polynomial involves applying the distributive property so that the monomial is multiplied with each term of the polynomial separately. This process requires careful management of coefficients and variable exponents to ensure that each term is correctly multiplied and the expression is properly simplified.

Sign Multiplication Rules

When multiplying terms that include negative numbers or variables with negative coefficients, it is important to apply the rules of sign multiplication. These rules state that the product of two numbers with the same sign is positive, while the product of numbers with different signs is negative. Managing these signs correctly is crucial to obtaining the right outcome during distribution and subsequent algebraic simplification.

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