Factoring and Evaluating Expressions

The video tutorial covers factoring expressions using models, the distributive property, and the greatest common factor (GCF). It explains how to use these concepts to write equivalent expressions and evaluate them with given variable values. The tutorial also highlights the equivalence of different expressions and provides examples with variables to reinforce understanding.

How many groups of five are present in the initial model discussed?

• Four

• Three

• Two

• One

What is the expression for two groups of five plus two groups of three?

• 2 * 5 + 2 * 3

• 2 + 5 + 3

• 2 * (5 + 3)

• 5 + 3 + 5 + 3

What property is used to show that 2 * (5 + 3) is the same as 2 * 5 + 2 * 3?

• Identity Property

• Distributive Property

• Commutative Property

• Associative Property

What is the greatest common factor of 3f and 3g?

• 2

• 3

• 1

• 6

How can 6x + 9y be factored using the greatest common factor?

• 6(x + y)

• 3(x + y)

• 3(2x + 3y)

• 9(2x + 3y)

What is the factored form of 24b + 8 using the GCF?

• 2(12b + 4)

• 12(2b + 1)

• 4(6b + 2)

• 8(3b + 1)

What is the equivalent expression for 7x + 7y?

• 7(x + y)

• x + y

• 7x + y

• x + 7y

If x = 3 and y = 4, what is the value of 6x + 21y?

• 102

• 84

• 90

• 126

What pattern is observed when evaluating equivalent expressions with different variable values?

• They always equal zero

• They are always different

• They evaluate to the same number

• They are always negative

How can knowledge of GCF and the distributive property help in rewriting expressions?

• By changing the variable

• By simplifying to factored form

• By adding more terms

• By making expressions longer