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Published byMilton Bence Modified over 2 years ago

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You can use algebra tiles to model algebraic expressions tile This 1-by-1 square tile has an area of 1 square unit. x -tile x 1 This 1-by- x square tile has an area of x square units. 3 x + 2 Area = 3(x + 2) x Area = 3(x ) + 3(2) Model the Distributive Property using Algebra Tiles 1-5 The distributive Property x + 2 +

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T HE D ISTRIBUTIVE P ROPERTY a(b + c) = ab + ac (b + c)a = ba + ca 2(x + 5)2(x) + 2(5)2x + 10 (x + 5)2(x)2 + (5)22x + 10 (1 + 5x)2(1)2 + (5x) x y(1 – y)y(1) – y(y)y – y 2 = = = = = = = = The product of a and (b + c): U SE THE D ISTRIBUTIVE P ROPERTY

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(y – 5)(–2)= (y)(–2) + (–5)(–2) = –2y + 10 –(7 – 3x)= (–1)(7) + (–1)(–3x) = –7 + 3x = –3 – 3x (–3)(1 + x) = (–3)(1) + (–3)(x) Simplify. Distribute the –3. Simplify. Distribute the –2. Simplify. –a = –1 a U SING THE D ISTRIBUTIVE P ROPERTY Remember that a factor must multiply each term of an expression. Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

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Find the difference mentally. Find the products mentally. The mental math is easier if you think of $11.95 as $12.00 – $.05. Write as a difference. You are shopping for CDs. You want to buy six CDs for $11.95 each. Use the distributive property to calculate the total cost mentally. 6(11.95) = 6(12 – 0.05) Use the distributive property. = 6(12) – 6(0.05) = 72 – 0.30 = The total cost of 6 CDs at $11.95 each is $ M ENTAL M ATH C ALCULATIONS S OLUTION

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S IMPLIFYING BY C OMBINING L IKE T ERMS Each of these terms is the product of a number and a variable.terms +–3y2y2 x +–3y2y2 x number +–3y2y2 x variable. +–3y2y2 x –1 is the coefficient of x. 3 is the coefficient of y 2. x is the variable. y is the variable. Each of these terms is the product of a number and a variable. x2x2 x2x2 y3y3 y3y3 Like terms have the same variable raised to the same power. y 2 – x 2 + 3y 3 – – 3x 2 + 4y 3 + y variablepower.Like terms The constant terms –5 and 3 are also like terms.

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Combine like terms. S IMPLIFYING BY C OMBINING L IKE T ERMS 4x – x 2 = (8 + 3)x Use the distributive property. = 11x Add coefficients. 8x + 3x = Group like terms. Rewrite as addition expression. Distribute the –2. Multiply. Combine like terms and simplify. 4x 2 – x = 3x – 2(4 + x) = 3 + (–2)(4 + x) = 3 + [(–2)(4) + (–2)(x)] = 3 + (–8) + (–2x) = –5 + (–2x) = –5 – 2x

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