Transcript
CHAPTER 2.5
The Distributive Property & Combining
Like Terms
Vocabulary:
terms: parts of an expression that are added together
coefficient: number part of a term with a variable part
like terms: have identical variable partsconstant term: a term that has no
variable
Example 3 Identify parts of an expression
Identify the terms, like terms, coefficients, and constant terms of the expression 3x 4 6x 2.– – +
SOLUTION
Write the expression as a sum: 6x–( )4 )3x –(+ + + 2
Terms: 6x,–3x, 4,– 2
Like terms: 3x and 6x;– 4 and 2–
Coefficients: 3, 6–
Constant terms: 4,– 2
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)
x 1 1
x 1 1
x 1 1
3(x) + 3(2)=
3x + 6=
Example
2 (x2 + 2x - 2) 2(x2) + 2(2x)=
2x2 + 4x=
Example
2(2)-
x2
x2
xx
x
x
-1-1
-1-1
- 4
Two practice problems
1. = 3 (2x2) – 3(10x) + 3(7)
2. = 6x2 – 30x + 21
1. = m (6x2) + m(4x) – m(12)
2. = 6x2m + 4xm – 12m
3 (2x2 – 10x + 7) =
m (6x2 + 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 + -12
-3 (2x + 4)=
-2(-1x) � -2(7)
= 2x ̶� -14
= 2x + 14
-2 (-x – 7) =
Example
-(-4x) + -(2)
= 4x + -2
- (-4x + 2) =
-12(x) � -12(4)
= -12x ̶� -48
= -12x + 48
-12 (x – 4)=
DISTRIBUTIVE PROPERTY
Whiteboard Races!!!
1. We are in teams of 3 or 4. 2. Mr. Becker will give us a problem and EVERYONE
will work it out silently on their boards for 30 seconds. 3. When Mr Becker says “team time”, we have an
additional minute to compare our problems with our teammates
4. We will only get a point if everyone has the answer correct .
5. When Mr Becker says 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)
2 (x + 3)
2x + 6
Problem 2
3 (4 + 5x)
3 (4 + 5x)
12 + 15x
Problem 3
-4(2x – 7)
-4(2x – 7)
-8x + 28
Problem 4
-2(8 + 4x)
-2(8 + 4x)
-16x – 8
Problem 5
- (3x – 5)
- (3x – 5)
-3x + 5
Problem 6
- (8 + 12x)
- (8 + 12x)
-8 – 12x
Problem 7
9 + 5(4x + 4)
9 + 5(4x + 4)
20x + 29
Problem 8
2x + 3(5 + 4x)
2x + 3(5 + 4x)
15 + 14x
Problem 9
2x + 3 – (x + 5)
2x + 3 – (x + 5)
x – 2
Problem 10
3x – (2x + 5) + 8
3x – (2x + 5) + 8
x + 3
Problem 11
4x – 2(3x – 3)
4x – 2(3x – 3)
-2x + 6
Problem 12
7x + 3 – (6x + 5)
7x + 3 – (6x + 5)
x – 2
Problem 13
a (2x + 3)
a (2x + 3)
2xa + 3a
NOW YOU’RE AT BAT. YOU ARE SITTING
SILENTLY WHILE I HAND OUT THE WORKSHEET.
THE END!
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