Exploring Equivalent Algebraic Expressions

Mrs. Vandenberg guides students through the process of writing equivalent algebraic expressions by factoring using the greatest common factor (GCF) and expanding using the distributive property. The lesson includes multiple examples, starting with simple expressions and advancing to more complex ones. Students are encouraged to use division ladders to find the GCF and verify their work using the distributive property. The video concludes with instructions for homework, emphasizing the importance of showing all work clearly.

What is the first step in finding the GCF of 3y + 15?

• Add the terms

• Multiply the terms

• Put the expression in a division ladder

• Use the distributive property

What is the GCF of 3y and 15?

• 1

• 5

• 3

• 15

How do you expand the expression 3(y + 5)?

• 3y + 5y

• 3y + 15

• 3y + 5

• 3 + 5y

What is the expanded form of 6(x + 9)?

• 6x + 9

• 6x + 6

• 6x + 54

• 6 + 9x

What is the GCF of 8k and 56?

• 16

• 8

• 2

• 4

What is the factored form of 8k + 56?

• 2(k + 28)

• 8(k + 7)

• 8(k + 8)

• 4(k + 14)

How do you verify that 8(k + 7) is equivalent to 8k + 56?

• By dividing the terms

• By subtracting the terms

• By adding the terms

• By using the distributive property

What is the GCF of 14a and 28b?

• 14

• 28

• 7

• 2

Which of the following is an equivalent expression to 16h + 40?

• 4(4h + 10)

• 2(8h + 20)

• All of the above

• 8(2h + 5)

Which expression is the GCF factored form of 16h + 40?

• 16(h + 2.5)

• 8(2h + 5)

• 4(4h + 10)

• 2(8h + 20)