Key Concepts

The Distributive Property

Definition:  the property used to find the product of a number/variable and a sum or difference.

Example:  a(b - c) = ab - ac

The number outside the parentheses is distributed to each part of the sum or difference in the parentheses.

Common mistakes:

1. Don't forget to multiply the number or variable outside the parentheses by both items in the parentheses
   Example:  5(x - 4) = 5x - 4;  a lot of people forget to multiply the number by both terms in the parentheses.  Should be 5(x - 4) = 5x - 20.
2. Be careful with negatives.  If the number outside is negative, you must distribute the negative with it.
   Example:  -3(x - 4) = -3x -12;  a lot of people forget to multiply -3 by -4.  Should be:  -3(x - 4) = -3x + 12

Combining Like Terms

If two terms have the same variable, to the same exponent, we call them like terms.

We can combine like terms by adding their coefficients.  The variables themselves don't change.

Example:  2x + 3y - 4x + 1y;  2x and -4x are like terms;  3y and 1y are like terms (keep the signs with the terms)
To combine the like terms, add their coefficients, so 2 + (-4) = -2; 3 + 1 = 4
Final answer:  -2x + 4y

Homework

pp. 99-100 #4-42 even, 50

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