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Distribution and like terms A look at the algebra behind algebra tiles….

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Combining like terms When combining like terms, add the coefficients on each group of like terms. Example 1: 6x + 5 + 2x With algebra 6x + 5 + 2x 8 positive x-bars and 5 positive units 8x + 5 With algebra tiles 6x + 5 + 2x Identify like terms. (6 + 2)x + 5 Add the coefficients on like terms. 8x + 5 Simplify.

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Example 2: 9x + 4 – 2x 9x + 4 + -2x Algebraically 9x + 4 – 2x Identify like terms. (9 + -2)x + 4 Combine the coefficients on like terms. 7x + 4 Simplify. 7 positive x-bars and 4 positive units 7x + 4 With algebra tiles 9x + 4 – 2x

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Example 3: 6x + 5 + -3x + -8 3 positive x-bars and 3 negative units 3x + -3 3x – 3 With algebra tiles Algebraically 6x + 5 + -3x + -8 Identify like terms. (6 + -3)x + (5 + -8) Add the coefficients on like terms. 3x + -3 3x – 3 Simplify.

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Example 4: 3(x + 5) Algebraically Distribute. Multiply. Simplify. Distribution Multiply the term outside the parentheses by each term inside the parentheses. 3 positive x-bars and 15 positive units 3x + 15 With algebra tiles 3(x + 5) Build 3 groups of 1x + 5. 3(x + 5) 3(x) + 3(5) 3x + 15

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Example 5: 2(3x – 1) Algebraically Distribute. Multiply. Simplify. 2(3x + -1) 2(3x) + 2(-1) 6x + -2 6x – 2 6 positive x-bars and 2 negative units 6x + -2 = 6x – 2 With algebra tiles 2(3x + -1) Build 2 groups of 3x + -1.

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Example 6: 2(x 2 – 2x + 1) Algebraically Distribute. Multiply. Simplify. 2(x 2 + -2x + 1) 2(x 2 ) + 2(-2x) + 2(1) 2x 2 + -4x + 2 2x 2 – 4x + 2 2 positive x 2 tiles, 4 negative x-bars, and 2 positive units 2x 2 + -4x + 2 = 2x 2 – 4x + 2 With algebra tiles 2(x 2 + -2x + 1) Build 2 groups of x 2 + -2x + 1.

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Example 7: 4(2x + 5) – 8 Distribution first. Identify like terms. 4(2x + 5) + -8 4(2x) + 4(5) + -8 8x + 20 + -8 8x + 12 Distribution and combining like terms 8x + (20 + -8) Simplify. Combine like terms.

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Example 8: -4 + 5(2x + 3) + x Distribution first. Identify like terms. -4 + 5(2x + 3) + x -4 + 5(2x) + 5(3) + 1x -4 + 10x + 15 + 1x 11x + 11 (10 + 1)x + (-4 + 15) Simplify. Combine like terms.

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§ 1.10 Properties of the Real Number System. Angel, Elementary Algebra, 7ed 2 Commutative Property Commutative Property of Addition If a and b represent.

§ 1.10 Properties of the Real Number System. Angel, Elementary Algebra, 7ed 2 Commutative Property Commutative Property of Addition If a and b represent.

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