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2.7 Distributive Property

2.7 Distributive Property. Distributive Property. This is the only property that has 2 different operations. It’s either multiplication and addition or multiplication and subtraction. To distribute means to “send out” or “give out”.

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2.7 Distributive Property

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  1. 2.7 Distributive Property

  2. Distributive Property This is the only property that has 2 different operations. It’s either multiplication and addition or multiplication and subtraction. To distribute means to “send out” or “give out”. There will ALWAYS be parenthesis. You “send out” the number in front of the parenthesis. 6*4 + 6*3 = 24 + 18 =42 Ex. 6(4 + 3) =

  3. Using the distributive property, we get the same answer we would have gotten if we followed the order of operations and did what was in parenthesis first. Ex. 6(4+3) 6(7) 42 6*4 + 6*3 = 24 + 18 =42 So why do we need the distributive property? Ex. 6(4 + 3) = Since we are working with variables, the terms in parenthesis won’t always be just numbers…

  4. The distributive property works the same way with variables. • Now try this one…

  5. Important vocab terms • Term – part of an expression, separated by addition or subtraction • Like terms – terms that have the exact same variable • Coefficient – a number before a variable • Constant – a number Ex. 5x2 + 3x + 6 + 2x This expression has 4 terms. The 5, 3 and 2 are coefficients. The 6 is a constant. 3x and 2x are like terms.

  6. Combining like terms • You can add or subtract terms if they have the exact same variable. • In order to be exactly the same, it must be the same letter, raised to the same exponent Ex. 4x2 and 5x are NOT like terms…they both have an x but one is squared & one is not. • 5x2 and 4x2 are like terms…they both have an x squared and they CAN be combined.

  7. Combining like terms Let’s practice combining the like terms: The first thing to do is identify the like terms…you can use shapes or colors if that helps you… • Combine 2x2+ 3x2 , 5x + 7x, 4 + 5 • The answer is 5x2 + 12x + 9

  8. Combining like terms Let’s practice combining the like terms: The first thing to do is identify the like terms… you can use shapes or colors if that helps you… Be careful with the signs!! • Combine 2x2+ 3x2 , -5x + 7x, 4 + -5 • The answer is 5x2 + 2x – 1

  9. Combining like terms Now you try one…combine the like terms:

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