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SAT MATH Lesson 12 Drill Day 12 Simplify the following expressions: 1. (3x3 yz2 )(5xy2 ) 4. (4xy2 )3 1 2 2 7. (4 x ) 2. 5. 8. 42a 3 2 7a 5a 2b 6 2 2 3. 8a 2bc3 2 4 24a b c 6. 16 y 2 9. 2 3 3 Algebraic Expressions Algebraic Expressions contain numbers, variables, and the symbols for operations. Since algebraic expressions themselves represent numbers they can be added, subtracted, divided and multiplied. Some examples of algebraic expressions are: b a b 3 x 7, 3x 1, y ab, , 6(2 x y ), r c 2 Like terms are terms that contain the same variables with corresponding variables having the same exponents. Simplify: 3x 2 2 x 2 x 2 5 x 4 The distributive property allows you to distribute multiplication over addition and subtraction. 8(4x + 7) = 8(4x) + 8(7) = 32x + 56 To evaluate and algebraic expression, substitute the numeric value of the variable in to the expression. Then evaluate the resulting numerical expression. Evaluate: 5 2a 3 when a = 2. Laws of Exponents Operation Rule Multiplication Add the exponents Examples (3a 2b3c)(2a 3b) 3 * 2 * a 23b33c 6a 5b 4c Division Subtract the exponents Power to a Power Multiply the exponents 4 x5 y 3 x4 5 8 12xy 3y (2a 2 )3 (21*3 a 2*3 ) 23 a6 8a6 Laws of Exponents Fractional Exponents Negative Exponents Examples