Simplifying Algebraic Expressions: A review of coefficients, constants, and Like Terms and Applying the Distributive Property so you can simplify.

Remember Algebraic Expressions? An Algebraic Expression -a group of numbers, symbols, and variables that express an operation or a series of operations. Anatomy of an Algebraic Expression: 2x + 7 coefficient variable constant the number in front a number without a variable of the variable Each separate piece of the expression, separated by + or - is called a term. 2x is a term and 7 is a term.

Example # 1 Simplify 3x + 6x x (3+6)x 9x Simplify by combining (adding) like terms Variable stays the same Add the coefficients Final Answer

Example 2-2c Simplify. 6x and –5x are like terms. 4 and –7 are also like terms. Find like terms Final answer Rewrite the subtraction = x - 3

Sometimes you have some extra work to do before you can combine like terms. m + 3(m + 2) = m + 3∙m + 3∙2 = m + 3m + 6 = 4m + 6 Distribute the 3 over the m and the 2 Combine like terms When you have a number outside of addition or subtraction in parenthesis, you should first use Distributive Property

Sometimes your distributive property gets more complicated with subtraction signs 3x – 4(x + 3) 3x + (-4)(x + 3) 3x + (-4)(x) + (-4)(3) 3x + -4x x x - 12 Rewrite the subtraction problem as an “ADD THE OPPOSITE” Use distributive property Combine like terms Simplify by getting rid of the two math symbols side by side (the + and - )

Example 2-2e Sometimes you have to use the distributive property to get rid of parenthesis before you can combine like terms. (multiply by 2) Remember –y = -1y: the Identity Property Distributive Property happens first. Find like terms Simplify.

Example 2-2g Answer: Simplify each expression. a. b. c. d. Answer:

Write these in your notebook and simplify each expression - 4(8x - 4) + 3x

Proper Order Remember that if you have coefficients and constants both in your answer, you need to rewrite it so the coefficients are first, and the constant is last. This is called simplifying. Failure to simplify will cost you half a point on each of your homework answers.

-5(x + 7) - 4

-2r - (3 - 4r)