AIMS Math Prep Jan 9-20 Evaluating expressions, simplifying expressions, compound interest formula

Evaluating Expressions An algebraic expression contains numbers, variables (letters) and operations (add, subtract, square, etc) To evaluate an expression, substitute the given values for each variable (letter).

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Example 7(2) 2 (3) 2 (4) 7(4)(9)(4)square 28(9)(4)multiply 252(4) 1008

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Example 5(-4) – 3(10) -20 –

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Example | (3)| | | |3| 3

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Simplifying Expressions Simplify an expression by combining like terms. Terms that have the same variables and exponents can be added/subtracted. Terms with different variables/exponents can be multiplied/divided When multiplying add the exponents When dividing subtract the exponents

Example Simplify the expression: 3x x + 5x – 3 Like terms: 3x + 2x + 5x = 10x 4 – 3 = 1 Solution: 10x + 1

Example Simplify the expression: 3x 4  5xy 3 The coefficients: 3(5) = 15 Variables: x 4  x = x 4+1 = x 5 Solution: 15x 5 y 3

Example Simplify the expression: 16x 4 y 2 ÷ 8xy 5 16 ÷ 8 = 2 x 4 ÷ x = x 4-1 = x 3 y 2 ÷ y 5 = y 2-5 = y -3 or 1/y 3 Solution 2x 3 y -3 or 2x 3 /y 3

Example Use the distributive property to simplify the expression. 4x(3x + 2y -1) Multiply each term by 4x =12x 2 + 8xy – 4x

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Example Distribute 15x 2 + 6x 2 y – 18x Hint: x(x) = x 2

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Example 12 ÷ -3 = -4 p 8 ÷ p = p 8-1 = p 7 x 6 ÷ x 4 = x 6-4 = x 2 -4p 7 x 2

Compound Interest Formula