Скачать презентацию 1 -5 The distributive Property You can use Скачать презентацию 1 -5 The distributive Property You can use

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

USE THE DISTRIBUTIVE PROPERTY The product of a and (b + c): a(b + USE THE DISTRIBUTIVE PROPERTY The product of a and (b + c): a(b + c) = ab + ac 2(x + 5) = 2(x) + 2(5) = 2 x + 10 (b + c)a = ba + ca (x + 5)2 = (x)2 + (5)2 = 2 x + 10 y(1 – y) = y(1) – y(y) = y – y 2 (1 + 5 x)2 = (1)2 + (5 x)2 = 2 + 10 x

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

MENTAL MATH CALCULATIONS SOLUTION You are shopping for CDs. You want to buy six MENTAL MATH CALCULATIONS SOLUTION You are shopping for CDs. You want to buy six CDs for $11. 95 each. 6(11. 95) = 6(12 – 0. 05) The mental math is easier if you think of $11. 95 as $12. 00 – $. 05. Write 11. 95 as a difference. = 6(12) – 6(0. 05) Use the distributive property to calculate the total cost = 72 – 0. 30 mentally. Use the distributive property. = 71. 70 Find the difference mentally. Find the products mentally. The total cost of 6 CDs at $11. 95 each is $71. 70.

SIMPLIFYING BY COMBINING LIKE TERMS Each of these terms is the product of a SIMPLIFYING BY COMBINING LIKE TERMS Each of these terms is the product of a number and a variable. terms number variable. – x + 3 y 2 – 1 is the x is the y is the 3 coefficient ofsame variable raised to the same power. variable. x. variable. y 2. power. coefficient of Like terms have the Like terms y 2 – x 2 + 3 y 3 – 5 + 3 – 3 x 2 + 4 y 3 + y The constant terms – 5 and 3 2 also like terms. are 3 2 3 x y

SIMPLIFYING BY COMBINING LIKE TERMS 8 x + 3 x = (8 + 3)x SIMPLIFYING BY COMBINING LIKE TERMS 8 x + 3 x = (8 + 3)x = 11 x 4 x 2 + 2 – x 2 = 4 x 2 – x 2 + 2 = 3 x 2 + 2 3 – 2(4 + x) = 3 + (– 2)(4 + x) Use the distributive property. Add coefficients. Group like terms. Combine like terms. Rewrite as addition expression. = 3 + [(– 2)(4) + (– 2)(x)] Distribute the = 3 + (– 8) + (– 2 x) Multiply. = – 5 + (– 2 x) Combine like terms and simplify. = – 5 – 2 x – 2.