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Algebra I Chapter 1-5 Distributive Property
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Warm - Up Do the odd problems on the EVALUATING EQUATION worksheet. COPY THE PROBLEMS ON YOUR PAPER AND SOLVE THEM. PLEASE DO NOT WRITE ON MY COPY.
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Group Work Formulas for the perimeter of a rectangle are used often by surveyors in designing land plots. One surveyor used Formula A; another used Formula B. Do both formulas give the same number for the perimeter? Formula A: P = 2l + 2w Formula B: P = 2(l + w)
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Commutative, Associative and Identity Properties Quiz State the property each equation represents. 1. 4 + (3 + 2) = (4 + 3) + 2 2. 5 + 3 = 3 + 5 3. 3(5 1) = (3 5)1 4. 7(3) = 3(7) 5. 6(4 + 3) = 6(3 + 4)
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Vocabulary Distributive Property – 2(x + y) = 2x + 2y We use the distributive property to clear parentheses
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Examples Use the Distributive Property to write an equivalent expression. 1. 3(x + 2) 2. (s + t + w)6 3. 4(2s + 5)
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Try This Use the distributive property to write an equivalent expression. 1. 4(x + y + z) 2. (y + 3)5 3. (8a + 3)2 1. 6(x + 2y + 5)
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Factoring If you reverse the distributive property, we have a process called factoring. ab + ac = a(b + c) EXAMPLES 3x + 3y 5x + 5y + 5z 7y + 14 + 21z 9x + 27 + 9
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Try This … Factor 5. 5x + 10 6. 12 + 3x 7. 6x + 12 + 9y 8. 5x + 10y + 5
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Factor and Check by Multiplying 5x + 10 2x + 4y 4a + 4
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Collecting Like Terms Vocabulary Terms – in an expression like 6s + 6t + 6w, 6s, 6t, and 6w are terms. Like Terms – Terms such as 5x and 4x, whose variable factors are exactly the same.
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Examples … Collecting Like Terms 3x + 4x x + x 2x + 3y + 5x + 2y 5x ² + x ²
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Try This Collect Like Terms 9. 6y + 2y 10. 7x + 3y + 5y + 4x 11. 10p + 8q + 4p + 5q 12. 7x ² + x ²
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