The Distributive Property. A (B + C) = AB + AC -A (B + C) = -AB - AC The distributive property says that a number next to the parentheses can be multiplied.

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The Distributive Property

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Presentation transcript:

The Distributive Property

A (B + C) = AB + AC -A (B + C) = -AB - AC The distributive property says that a number next to the parentheses can be multiplied by each number inside the parentheses.

Example 5(3)+5(4) =15+20 =35 5 (3 + 4)= 4(-1)+4(3) =-4+12 =8 4 (-1+ 3)=

Example 3(5)+3(6) =15+18 =33 3 (5 + 6)= 2(-1)+2(5) =-2+10 =8 2 (-1 + 5)=

3 (x + 2) x11 x11 x11 3(x)+3(2)= 3x+6= Example

2 (x 2 + 2x - 2) 2(x 2 )+2(2x)= 2x 2 +4x= Example 2(2)- x2x2 x2x2 x x x x -4

Two practice problems 1. = 3 (2x 2 ) – 3(10x) + 3(7) 2. = 6x 2 – 30x = m (6x 2 ) + m(4x) – m(12) 2. = 6x 2 m + 4xm – 12m 3 (2x 2 – 10x + 7) = m (6x 2 + 4x – 12) =

Notes When multiplying by a negative number, use the distributive property and follow the rules for multiplying integers + + = + or - - = + (same signs = positive) - + = - or + - = - (opposite signs = negative)

Example -3(2x)+-3(4) =-6x (2x + 4)= -2(-1x) ̶ -2(7) =2x ̶ -14 =2x (-x – 7)=

Example -(-4x)+-(2) =4x+-2 - (-4x + 2)= -12(x) ̶ -12(4) =-12x ̶ -48 =-12x (x – 4)=

Practice Activity

DISTRIBUTIVE PROPERTY Whiteboard Race! 1.We are in teams of 3 or 4. 2.I will give you a problem and EVERYONE will work it out silently on their boards for 30 seconds. 3.When I say “team time”, you have an additional minute to compare problems with your teammates 4.A team will only get a point if everyone has the answer correct. 5.When I say boards up, all boards go up. Any team who does not have all boards up with correct answers cannot score a point.

Problem 1 2 (x + 3)

2x + 6

Problem 2 3 (4 + 5x)

x

Problem 3 -4(2x – 7)

-8x + 28

Problem 4 -2(8 + 4x)

-16x – 8

Problem 5 - (3x – 5)

-3x + 5

Problem 6 - (8 + 12x)

-8 – 12x

Problem (4x + 4)

20x + 29

Problem 8 2x + 3(5 + 4x)

x

Problem 9 2x + 3 – (x + 5)

x – 2

Problem 10 3x – (2x + 5) + 8

x + 3

Problem 11 4x – 2(3x – 3)

-2x + 6

Problem 12 7x + 3 – (6x + 5)

x – 2

Problem 13 a (2x + 3)

2xa + 3a