Question

Multiply. See Examples 4 and 5. $$ (5 x-3)(2 x-3) $$

   Multiply. See Examples 4 and 5.
$$
(5 x-3)(2 x-3)
$$

Elementary and Intermediate Algebra

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 5, Problem 48

Instant Answer

Solved by Expert Melissa Stefan

03/22/2020

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That is, $5x$ times $2x$ which equals $10x^2$. Show more…

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Multiply. See Examples 4 and 5. $$ (5 x-3)(2 x-3) $$

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Key Concepts

Combining Like Terms

After applying the distributive property or the FOIL method, the resulting expression often contains similar terms. Combining like terms involves adding or subtracting coefficients of terms that share the same variable parts, which simplifies the expression to its most concise form.

Polynomial Multiplication

Polynomial multiplication involves calculating the product of two or more polynomials. This process relies on the distributive property to ensure that every term in the first polynomial is multiplied by every term in the second, and then combining like terms to arrive at a simplified expression.

Distributive Property

The distributive property is an essential algebraic rule used to multiply a single term by each term within a parenthesis, which is fundamental when multiplying two algebraic expressions. This property ensures that every term in one polynomial is multiplied by every term in the other, facilitating the expansion process of expressions like binomials.

FOIL Method

The FOIL method is a specific application of the distributive property for multiplying two binomials. It stands for First, Outer, Inner, Last, referring to the order in which the products of terms are calculated. This systematic approach aids in ensuring that no term is overlooked, resulting in a correctly expanded polynomial.

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