Warmup #9
Use the Distributive Property to simplify each:
1.
= 3 • 5x − 3 • 4
= 15x − 12
2.
−3( 4 − 2x )
4.
= −3 • 4 − ( −3) • 2x
= −12 − ( −6x )
= −12 + 6x
(
4 ( 2x + 3)
3( 5x − 4 )
5.
= 4 ( 2x ) + 4 ( 3)
2 3x 2 − 5x + 4
3.
)
= 2 • 3x 2 − 2 • 5x + 2 • 4
= 8x + 12
= 6x 2 − 10x + 8
13( 98 )
21(104 )
= 13(100 − 2 )
= 1300 − 26
= 1274
6.
= 21(100 + 4 )
= 21(100 ) + 21 • 4
= 2100 + 84 = 2184
Notes #9 Sec. 1.7 The Distributive Property (the rest)
Goal: Simplify expressions by combining like terms.
From yesterday:
Like terms have the same variables and exponents. They may be added or subtracted.
Unlike terms don’t. They can’t.
In algebra,
• terms are things that are added and subtracted
• factors are things that are multiplied, and
coefficients are the numbers in front of variables.
In the expression 5x 2 − 3x + 2 , the terms are: 5x 2 , − 3x, and 2 (bring the signs with them)
• the coefficient of the first term is 5
• the coefficient of the second term is –3 (bring the sign), and
• 2 is called the constant term.
Constant means unchanging.
To combine like terms, add their coefficients (the numbers in front.)
5x + 2x =
4x − 7x =
3 − 2x + 5 = 8 − 2x
4x − 3 + 2x − 8 =
3( 2x − 5 ) + 2 =
5x 2 − 3x + 4 + 2x 2 + 5x − 9 =
When you see the word “quantity” it means that you have two or more terms inside parenthesis.
Three times the quantity x plus 4 3( x + 4 )
Seven times the sum of 8 and n 7 ( 8 + n )
-2 times the quantity t plus 7 −2 ( t + 7 )
Four times the difference of 8 and a number 4 ( 8 − n )
Sec. 1.8 Properties of Real Numbers
The Commutative Property (you can add/multiply in any order)
Addition
Multiplication
a+b=b+a
a•b=b•a
3+8=8+3
5•4=4•5
The Associative Property (you can group addition/multiplication either way)
Addition
Multiplication
a + (b + c ) = ( a + b ) + c
a (b • c ) = ( a • b ) c
5 + (3 + 2) = (5 + 3) + 2
3(4 • 5) = (3 • 4)5
Identity Properties
Addition (the additive identity = 0)
a+0 = a
5+0=5
Multiplication (the multiplicative identity = 1
a •1 = a
3•1=3
Inverse Properties
Addition (opposites are additive inverses) Multiplication (reciprocals are mult. Inverses)
1
a + ( −a ) = 0
a• =1
a
1
3 + ( −3) = 0
5• =1
5
Don’t forget the Distributive Property from yesterday: a ( b + c ) = ab + ac
5 ( 5 − 2x ) = 25 − 10x
Tell which property is represented. Be sure to tell if it is a property of multiplication or addition.
1.
5+7 = 7+5
2.
3( 2 • 7 ) = ( 3 • 2 ) • 7
3.
2 ⎛ 3⎞
⎜ ⎟ =1
3⎝ 2⎠
4.
p+q = q+ p
5.
5 ( 2x − 5 ) = 10x − 25
6.
3 + 5 − 4a = 5 + 3 − 4a
7
( −3 + 4 ) + 5 = −3 + ( 4 + 5 )
8.
−14 • 0 = 0
9.
5 + 3( 2x − 3) = 5 + 6x − 9
10.
−8 + 0 = −8
Homework #9 Sec. 1.7: 35-48 all, start studying vocabulary for your test Friday