Simplifying Algebraic Expressions Unit 1 ~ Intro to Algebra Simplifying Algebraic Expressions

Simplifying Algebraic Expressions There are two things that you must be able to do when simplifying algebraic expressions . . . The first is to be able to use the distributive property. The second is to be able to combine like terms.

Distributive Property Multiply across the parentheses – each element inside the parentheses is multiplied by the element outside the parentheses.

Simplified Expression Examples . . . Expression Simplified Expression 3(x + 7) = 3(4x – 5) = -2(x – 4) = 20(x + ¼) = 3x + 21 12x - 15 -2x + 8 20x + 5

Can you identify 3 sets of like terms? Combining Like Terms Like terms are two or more terms that have EXACTLY the same variables. 2x 5y 7 6y Can you identify 3 sets of like terms? 4 8x 3xy 4x2

Combining Like Terms To combine like terms, add or subtract the coefficients. DO NOT change the variable. EXAMPLE: 9x - 3y + 4x + 2y 9x - 3y + 4x + 2y 13x - 1y 13x - y

More examples . . . 2(x + 4) + 3(x – 5) – 2y 2x + 8 + 3x – 15 – 2y 5x – 7 – 2y 3(ab – a) – 2(b – a) – 4ab 3ab – 3a - 2b + 2a – 4ab - ab – a – 2b