Exploring Multiplying Polynomials

This video tutorial teaches how to multiply polynomials using the FOIL method, a mnemonic for multiplying the First, Outer, Inner, and Last terms. It provides three examples: simplifying (3x - 5)(2x + 7), (x - 7)(5x + 6), and expanding (6r + 8)^2. Each example is broken down step-by-step, demonstrating the multiplication and combination of like terms to reach the final simplified expression.

What does FOIL stand for in polynomial multiplication?

• First, Outer, Inner, Last

• First, Open, Inner, Loop

• First, Outer, Inner, Linear

• Final, Outer, Inner, Last

What is the result of multiplying the first terms of 3x and 2x?

• 5x^2

• 6x

• 5x

• 6x^2

After combining like terms, what is the coefficient of x in the product of (3x - 5) and (2x + 7)?

• 11

• 21

• -10

• 35

What is the final step in simplifying the product of two polynomials?

• Square the last term

• Multiply the first terms

• Combine like terms

• Multiply the outer terms

In the example of (x + 6)(x - 7), what is the coefficient of the linear term in the simplified form?

• -1

• 6

• -7

• 1

What is the constant term in the product of (x + 6) and (x - 7)?

• 7

• -6

• 42

• -42

When squaring a binomial, such as (6r + 8)^2, what is the first step?

• Square the last term

• Combine like terms

• Multiply the binomial by itself

• Square the first term

What is the coefficient of the linear term in (6r + 8)^2?

• 96

• 64

• 48

• 36

What is the constant term in the expansion of (6r + 8)^2?

• 36

• 96

• 64

• 48

What is the result of squaring the binomial (6r + 8)?

• 36r^2 + 96r + 64

• 48r^2 + 96r + 64

• 36r^2 + 96r - 64

• 36r^2 + 48r + 64