Multiply: (3 x+5)(2 x-7).

Name: Problem 120, Chapter 7: Introductory and Intermediate Algebra for College Students 4th
Uploaded: 2020-06-08T22:40:26-08:00
Duration: 41 s
Channel: Brandon Fox
Description: Multiply: (3 x+5)(2 x-7).

Key Concepts

Combining Like Terms

After multiplying the terms in polynomial multiplication, the resulting expression often contains like terms. Combining like terms—the process of summing coefficients of the same variable raised to the same power—streamlines the expression and is crucial for achieving the simplest form of the polynomial.

FOIL Method

The FOIL method is a specific application of the distributive property for multiplying two binomials. FOIL stands for First, Outer, Inner, and Last, referring to the pairs of terms that are multiplied together. This method helps organize and execute the multiplication process methodically before simplifying the result.

Polynomial Multiplication

This concept involves multiplying expressions that have more than one term. It requires understanding how each term in the first polynomial interacts with each term in the second polynomial, ensuring that no term is left unmultiplied. In multiplying polynomials, the goal is typically to simplify the expression by combining all like terms into a single, more compact form.

Distributive Property

The distributive property is a fundamental principle in algebra that allows multiplication to be distributed over addition or subtraction. In the context of multiplying polynomials, this means multiplying each term of one binomial by every term of the other binomial, which is the underlying process used in techniques such as the FOIL method.

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