Multiplying and Identifying Polynomials

The video tutorial covers the concept of multiplying binomials, starting with an introduction to binomials and their structure. It explains the process of multiplying binomials using the distributive property, followed by practice problems with step-by-step solutions. The tutorial also explores advanced multiplication involving binomials with different variables and concludes with a summary of key points.

What is a binomial?

• A single term with a variable

• A set of two monomials joined by addition or subtraction

• A number without variables

• A polynomial with three terms

Which of the following is an example of a binomial?

• 3x^2

• 7x + 6y

• 5

• x^3 - 2x^2 + x

What method is preferred by the teacher for multiplying binomials?

• Trial and error

• FOIL method

• Graphical method

• Distributive property

What does the distributive property state?

• Multiply the first term by the second term

• Add all terms together

• Divide the terms by each other

• Multiply each term in the first set of parentheses by each term in the second set

In the example 3x * (7x + 3), what is the first step?

• Multiply 3x by 7x

• Add 3x and 7x

• Divide 3x by 7x

• Subtract 3 from 7x

What is the result of multiplying 3x by 7x?

• 10x^2

• 10x

• 21x^2

• 21x

What happens to the middle terms in the example 3x * (7x + 3) + (-2) * (7x + 3)?

• They are ignored

• They are subtracted

• They are added

• They are combined as like terms

In the practice problem using arrows, what is the result of 2G * 3G?

• 5G^2

• 6G^2

• 6G

• 5G

What is the final trinomial in the practice problem with arrows?

• 6G^2 + 5G - 4

• 6G^2 - 5G + 4

• 6G^2 + 5G + 4

• 6G^2 - 5G - 4

In the color-coded problem, what is the result of 4a * 5a?

• 28a

• 20a

• 28a^2

• 20a^2