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2(x + 3)

2(x + 3). Distributive property - used to multiply a single term and two or more terms inside a set of parentheses. . Distributive Property. Recall the distributive property of multiplication over addition . . . symbolically: a × (b + c) = a × b + a × c. Distributive Property.

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2(x + 3)

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  1. 2(x + 3) Distributive property - used to multiply a single term and two or more terms inside a set of parentheses.

  2. Distributive Property Recall the distributive property of multiplication over addition . . . symbolically: a × (b + c) = a × b + a × c

  3. Distributive Property For any numbers a, b & c, it is true that a(b + c) = ab + ac Example: If we do the parenthesis first (PEMDAS) 2(2 + 5) = 2(7) = 14 or 2(2 + 5) = 2(2) + 2(5) = 14

  4. Example 2 (3x + 4) 2 (3x + 4) 6x +8 Rainbow Arrows!

  5. Practice 6(2 quarters + 3 nickels) = 12 quarters + 18 nickels = $3.90 5(3a + 2b) 15a + 10b 2(3n – 4) 6n - 8

  6. Variables Multiplied by Variables Remember w * w = w2 - Not 2w! Distribute X(x + 3) x(y – 6) X2 + 3xxy – 6x

  7. Distributing a Negative -2(3x – 4) -2(3x – 4) -6x + 8 What is a negative times a positive? Negative times a negative?

  8. Stop for today Coming up! Combining Like Terms! Yea!

  9. Like Terms Terms that have the EXACT same variables or no variables. Example: 2x x -3x Like terms. 2x 4x2 3xy 2 NOT like terms. Why?

  10. Combining Like Terms If there are Like Terms, you can (and should) combine them to make a simpler expression. Example: 3x – x + 6x = 8x Try one 7b – 2b + 3b = 8b

  11. Practice -2x2 + 7x 2x2 + 3x– 4x2 + 4x = 3xy + 2x + 3xy– 6x2– 2x2 = -8x2 + 6xy + 2x

  12. Distributive Property and Combining Like Terms 4(x-4) + 2x – 6 4x -16 + 2x – 6 First, distribute the 4 6x – 16 – 6  then, combine the x 6x - 22  then combine the constants

  13. Another Example 12x – 6(x + 3) -5x + 2  what to distribute? 12x – 6x -18 -5x + 2  combine like terms 12x – 6x -18 -5x + 2 1x -18 + 2  combine constants 1x -16 or x -16  final answer

  14. Practice! 4x -2(x + 6) 4x – 2x – 12 2x -12  Final answer 22x + 3(x – 9) 22x + 3x – 27 25x -27  Final answer

  15. Challenge 4y + 4(y-7) + 2(x+3) 4y + 4y – 28 + 2x + 6 8y – 28 + 2x + 6 8y - 22 + 2x  final answer

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