Distributive Property and Simplifying Expressions

This video tutorial covers the use of the distributive property and combining like terms to simplify algebraic expressions. The instructor emphasizes the importance of using the sign in front of terms during distribution and combination. Through a series of examples, the video demonstrates how to handle negative signs, imaginary numbers, and multiple distributive properties. The tutorial also suggests using color coding to help visualize the process, making it easier to follow along and understand the steps involved in simplifying expressions.

What is the main purpose of using the distributive property in algebraic expressions?

• To add numbers

• To simplify expressions

• To multiply numbers

• To divide numbers

In the first example, what is the result of distributing -3 across the expression (1 - 4x)?

• -3 - 12x

• 3 + 12x

• -3 + 12x

• 3 - 12x

When combining like terms, what should you do if the terms have different signs?

• Subtract the numbers

• Divide the numbers

• Add the numbers

• Multiply the numbers

In the second example, what is the simplified form of the expression after distributing the imaginary negative one?

• 4x + 6

• -4x - 6

• 4x - 6

• -4x + 6

What happens to terms that simplify to zero in an expression?

• They are ignored in the final result

• They are multiplied in the final result

• They are subtracted from the final result

• They are added to the final result

In example 3, what is the result of combining -8x, 3x, and 5x?

• 0x

• 2x

• 1x

• -1x

In example 4, what is the result of distributing -4 across the expression (1x - 2)?

• -4x - 8

• 4x + 8

• 4x - 8

• -4x + 8

What is the final simplified form of the expression in example 4?

• x - 20

• x + 20

• -x + 20

• -x - 20

In example 5, what is the result of distributing -2 across the expression (n - 4)?

• -2n - 8

• 2n - 8

• 2n + 8

• -2n + 8

What is the final simplified form of the expression in example 5?

• -5n - 5

• 5n + 5

• 5n - 5

• -5n + 5