Review of the Distributive Property of Multiplication Notes

What is the distributive property?Distributive property – a mathematical property used to rewrite expressions involving addition or subtraction and multiplication.

Ex #1: a(b – c) rewrite as a(b + (-c)) a (b) + a (-c) ab – ac

Ex #2: 2(x + 1) 2 x + 2 1∙ ∙

2x + 2

Recall – Solving Linear Equations (isolate the variable)• You must use the properties of equality to solve an equation. Ex #1 2x + 5 = 13 - 5 - 5 (subtract 5 from each sides) 2x = 8 (divide each side by 2) 2 2 x = 4

Example #27x + 2 = 9x + 3 7x + 2 = 9x-7x -7x (subtract 7x from each side) 2 = 2x + 3 (subtract 3 from each side) - 3 -3 -1 = 2x (divide each side by 2) -1 = 2x 2 2 -½ = x

Multi-step equations (w/distributive property)Use the distributive propertyExample #1 3(x + 5) 3(x) + 3(5) 3x + 15Example #2 2(3x –10) Rewrite as 2(3x + (-10)) 2(3x) + 2(-10)

6x – 20Example #3 -(x - 5) Rewrite as -1(x + (-5)) -1(x) + (-1)(-5) -1x + 5Now, try thesea) -4(x – 4) b) 10(x + 10)c) 7(x – 3) d) -(-x – 1)

Solutions to “Try These”Now, try thesea) -4(x – 4) Rewrite as -4(x + (-4)) -4(x) + -4(-4) -4x + 16b) 10(x + 10) 10 x + 10 10∙ ∙ 10x + 100c) 7(x – 3) Rewrite as 7(x + (-3)) 7 x + 7(-3)∙ 7x + (-21) OR 7x – 21 d) -(-x – 1)Rewrite as -1(-1x + (-1)) (-1)(-1x) + (-1)(-1) 1x + 1 OR x +1

Solving Multi-step Equations (isolate the variable)Additional examples:

Ex #4 2g + 3(g + 1) = 13 (distribute 3 to everything in parenthesis)

2g + 3(g) + 3(1) = 13

2g + 3g + 3 = 13 (combine like terms) 5g + 3 = 13

- 3 -3 (subtract 3 from each side) 5g = 10 (divide each side by 5) 5 5 g = 2Ex #5 x + x + x + 3x = 24 (combine like terms) 6x = 24 (divide each side by 6) 6 6 x = 4

Vocabulary TermsDistributive Property - a mathematical property used to rewrite

expressions involving addition or subtraction and multiplication.Terms – the parts of an expression separated by addition or subtraction.

Ex. 2x +3 ( 2x and 3 are the terms)Like terms – terms in an expression with the same variable raised to the

same power. Ex. x3 + x2 + 3x3 (3x3 & x3 are like terms)

Variable – a letter that represents an unknown numberProperties of equality- whatever operation is done to one side of an

equation must be done to the other to isolate the variable.Isolate – to get alone on one side of the equal sign.Equivalent Expressions - expressions of different forms that can be

proven equal by substituting a number for the unknown. Ex. 4x + 4 , 4(x+1) and x + x +x +x + 4 are equivalent

expressions