Combining Like Terms and Creating Equivalent Expressions

This video tutorial covers the concept of combining like terms to create equivalent expressions. It begins with an introduction to key vocabulary, such as terms, variables, and constants. The video explains how to identify like terms and the process of combining them using addition. It provides step-by-step examples, demonstrating the simplification of expressions and the application of the distributive property. The tutorial concludes with a practice problem for viewers to solve, reinforcing the concepts learned.

What is a term in a mathematical expression?

• A combination of different variables.

• A variable with a coefficient.

• A single constant or variable, or the product of numbers and variables.

• A number raised to a power.

Which of the following pairs are like terms?

• 7y^2 and 8y^2

• 5x and 5x^2

• 2 and 2x

• 3x and 3y

What is the first step in simplifying equivalent expressions?

• Apply the distributive property if necessary.

• Annotate the like terms.

• Combine like terms.

• Rewrite subtraction as addition.

What does the commutative property of addition state?

• a + b = b + a

• a * b = b * a

• a + b = a - b

• a / b = b / a

In the expression 5x + (-4) - 6x + 2x - 3 + 8x^2, which terms are like terms?

• 5x, -4, -3

• 5x, -6x, 2x

• -4, -3, 8x^2

• 5x, 8x^2

What is the simplified form of 5x + (-4) - 6x + 2x - 3 + 8x^2?

• 1x + 8x^2

• 8x^2 - 7

• 1x - 7

• 1x - 7 + 8x^2

What is the result of distributing -3 in the expression -3(y - 4)?

• -3y + 12

• -3y - 12

• 3y - 12

• 3y + 12

What is the simplified form of -3(y - 4) + 5 + 3y?

• 17

• 12

• 5

• 0

What is the equivalent expression of 4(-2x - 5) + 12 - 4x?

• -12x - 8

• -12x + 8

• -8x + 12

• -8x - 20

What is the first step in solving 4(-2x - 5) + 12 - 4x?

• Distribute the 4.

• Annotate the like terms.

• Rewrite subtraction as addition.

• Combine like terms.