The Distributive Property | Simplifying Expressions | Math with Mr. J

Summary

This video by Math with Mr. J explains how to simplify algebraic expressions using the distributive property. It covers how to remove parentheses when terms inside cannot be combined, demonstrating with various examples involving positive and negative numbers and different variables.

Highlights

Introduction to the Distributive Property00:00:04

The distributive property helps remove parentheses in algebraic expressions when terms inside cannot be combined. It involves multiplying the term outside the parentheses with each term inside. This video focuses solely on removing parentheses; later videos will cover combining like terms.

Example 1: Positive Multiplier00:01:12

For the expression 9(3C + 2), distribute 9 to both 3C and 2. This results in (9 * 3C) + (9 * 2), which simplifies to 27C + 18. Since there are no like terms, this is the simplified expression.

Example 2: Multiplier with Subtraction (Method 1)00:01:54

For 4(-6y - 5), distribute 4 to -6y and then to 5, keeping the subtraction sign. (4 * -6y) - (4 * 5) gives -24y - 20. This is the simplified form as there are no like terms.

Example 2: Multiplier with Subtraction (Method 2)00:02:36

An alternative way to think about 4(-6y - 5) is to consider the -5 as a negative term. Distribute 4 to -6y and to -5. So, (4 * -6y) + (4 * -5) results in -24y - 20, yielding the same simplified expression.

Example 3: Negative Multiplier with Subtraction (Method 1)00:03:34

Given -2(-8x - 7y), distribute -2 to -8x and 7y. (-2 * -8x) - (-2 * 7y) becomes 16x - (-14y). To simplify the double sign, remember that subtracting a negative is equivalent to adding a positive, so the expression becomes 16x + 14y.

Example 3: Negative Multiplier with Subtraction (Method 2)00:05:03

Alternatively for -2(-8x - 7y), view the expression inside as -8x plus -7y. Distribute -2 to -8x and to -7y. (-2 * -8x) + (-2 * -7y) results in 16x + 14y, again demonstrating the same simplified answer.

Example 4: Positive Multiplier with Two Different Variables00:05:55

For 15(3G + H), distribute 15 to 3G and to H. This results in (15 * 3G) + (15 * H), which simplifies to 45G + 15H. Since G and H are unlike terms, the expression is simplified.