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The Distributive Property & Combining Like Terms

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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)2 2x + 10 (1 + 5x)2(1)2 + (5x) x y(1 + x) y(1) +y(x) y + xy U SING THE D ISTRIBUTIVE P ROPERTY = = = = = = = = The product of a and (b + c): BACK

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–(y – 5) = (y)(–1) + (–5)(–1) = –y + 5 –(7 – 3x) = (–1)(7) + (–1)(–3x) = –7 + 3x = –3 – 3x (–3)(1 + x)= (–3)(1) + (–3)(x) Simplify. Distribute the –3. Simplify. Distribute the –1. 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. BACK

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Like Terms are expressions that contain the same variable raised to the same power like 4mn and 7mn. Combine like terms. S IMPLIFYING BY C OMBINING L IKE T ERMS 4x x = 11x +y The 8x and 3x are like terms and can be combined. 8x + 3x + y = 4x 2 +1 x Group like terms. = 5x BACK

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Combine like terms with parenthesis… BACK

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Objectives Use the Distributive Property to solve equations. Solve real-world problems by using multistep equations.

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Key Skills Solve 3(x - 4) = 48 Use the distributive property. 3 * x + 3 * -4 = 48 Solve 3(x - 4) = 48 Multiply 3x - 12 = 48 Add both sides of the = sign x = 60 Divide both sides of the = sign by 3. 3 x = 20

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Key Skills Solve 5(x +2) = 35 Use the distributive property. 5 * x + 5 * 2 = 35 Solve 5(x +2) = 35 Multiply 5x + 10 = 35 Subtract 10 from both sides of the = sign x = 25 Divide both sides of the = sign by 3. 5 x = 5 TRY THIS

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Key Skills Solve 3y – 8 –y = 6 Combine like terms that are on the same side of the = sign. Solve 3y – 8 –y = 6 2y – 8 = 6 Add 8 to both sides of the = sign y = 14 Divide both sides of the equal sign by 2 2 y = 7

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Key Skills Solve 6y +2 –3y = 8 Combine like terms that are on the same side of the = sign. Solve 6y +2 –3y = 8 3y +2 = 8 Subtract 2 from both sides of the = sign. -2 3y = 6 Divide both sides of the equal sign by 3 3 y = 2 TRY THIS

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Key Skills Solve 4x -8(x + 1) = 8 Distribute -8 4x -8 * x + -8 * 1 = 8 Multiply 4x -8x -8 = 8 Combine like terms. 4x -8x -8 = 8 -4x -8 = 8 Add 8 to both sides of the = sign x = 16 Divide both sides of the equal sign by x = -4

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Key Skills Use the Distributive Property to solve multistep equations. Solve 8x – 2(3x – 4) = 5x – 7. 8x + (–2)(3x) + (–2)(–4) = 5x – 7 8x – 6x + 8 = 5x – 7 Distributive -2 Solve 8x – 2(3x – 4) = 5x – 7. Multiply. 8x – 6x + 8 = 5x – 7 Combine like terms that are on the same side of the = sign. 2x + 8 = 5x – 7

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Subtract 2x from both sides of the = sign. -2x 8 = 3x -7 Add 7 to both sides of the = sign = 3x Divide both sides of the = sign by = x

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Key Skills Use the Distributive Property to solve multistep equations. Solve 4y – 7(y +6) = 5y – 2. 4y + (–7)(y) + (–7)(+6) = 5y – 2 4y – 7y -42 = 5y – 2 Distributive -7 Solve 4y – 7(y +6) = 5y – 2. Multiply. 4y – 7y -42 = 5y – 2 Combine like terms that are on the same side of the = sign. -3y -42 = 5y – 2 TRY THIS

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-3y -42 = 5y – 2 Add 3y to both sides of the = sign. +3y -42 = 8y -2 Add 2 to both sides of the = sign = 8y Divide both sides of the = sign by = y

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