Question

Find each product. $$ (5 z+3)(2 z-3) $$

   Find each product. 
$$
(5 z+3)(2 z-3)
$$

Trigonometry

David I. Schneider;… 12th Edition

Chapter 0, Problem 48

Instant Answer

Solved by Expert Nick Johnson

02/19/2023

Step 1

This means we multiply each term in the first binomial by each term in the second binomial. So, we get $(5z \times 2z) + (5z \times -3) + (3 \times 2z) + (3 \times -3)$. Show more…

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Find each product. $$ (5 z+3)(2 z-3) $$

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Key Concepts

Combining Like Terms

Once the products of the individual terms have been computed, combining like terms is the next step in simplifying the expression. This process involves adding or subtracting coefficients of terms that have the same variable raised to the same power, which reduces the expression to its simplest form.

FOIL Method

The FOIL method is a specific application of the distributive property for multiplying two binomials. It stands for First, Outer, Inner, Last, representing the order in which pairs of terms are multiplied to ensure every term from one binomial is multiplied by every term of the other.

Polynomial Multiplication

Polynomial multiplication is the process of multiplying each term of one polynomial by each term of another, ensuring that all resulting products are correctly computed before simplification. This process underlies most algebraic manipulations when dealing with expressions containing one or more variables.

Distributive Property

The distributive property allows one to multiply a single term by a sum or difference inside parentheses, stating that a(b + c) equals ab + ac. This principle is essential when expanding products of binomials or larger polynomials.

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