Properties of Multiplication and Simplification

The video tutorial explains how to multiply polynomials, focusing on distributing each term of one polynomial into another. It demonstrates this process with a trinomial and a binomial, showing how to handle each term systematically. The tutorial also highlights the commutative property of multiplication, verifying that changing the order of multiplication does not affect the result. The video concludes by combining like terms to simplify the expression, ensuring the same result is achieved regardless of the multiplication order.

What is the first step in multiplying a trinomial by a binomial?

• Add the coefficients

• Distribute each term of the trinomial into the binomial

• Subtract the exponents

• Divide the terms

How many products result from distributing a trinomial into a binomial?

• Six

• Five

• Seven

• Four

What is the result of combining like terms in the expression 6x^3 + 14x^2 - 33x + 14?

• 6x^3 + 14x^2 - 33x + 14

• 6x^3 + 18x^2 - 21x + 14

• 6x^3 + 12x^2 - 33x + 14

• 6x^3 + 14x^2 - 21x + 14

What property allows us to change the order of multiplication without affecting the product?

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

What is the result of multiplying 3x by 2x^2?

• 6x^2

• 5x^2

• 6x^3

• 5x^3

What is the result of multiplying -2 by -7?

• 14

• -9

• 9

• -14

What is the simplified form of 18x^2 - 4x^2?

• 14x^2

• 22x^2

• 12x^2

• 16x^2

What is the result of combining -12x and -21x?

• -9x

• -33x

• -31x

• -29x

What is the final constant term in the expression after simplification?

• 14

• 16

• 18

• 12

Why does changing the order of multiplication not affect the product?

• Because of the Commutative Property

• Because of the Identity Property

• Because of the Distributive Property

• Because of the Associative Property