Algebra 1 Common Core Student Edition, Grade 8-9

Tliink...............
How do you read
expressions like
3(x + 8)?
Read an expression
inside parentheses as
"the quantity." Read
3(x + 8) as "3 times
the quantity x plus 8."

How can you get
started?
Think of division as
multiplying by the
reciprocal. So change
the division by 5 to
multiplication by

What does the
negative sign in front
of the parentheses
mean?
It indicates the opposite
of the entire expression
inside the parentheses.

I S i m p l i f y i n g E x p r e s s i o n s

What is the simplified form of each expression?

Q 3(jc + 8) 0 (5b - 4)( - 7)

3(x + 8) = 3(x) + 3(8) Distributive Property (5b - 4)(—7) = 5b(-7) - 4(—7)

= 3x + 24 Simplify. = -35 b + 28

4 G o t It? 1. W h a t is th e s i m p li f i e d f o r m o f e a c h e x p re s s io n?

a. 5(x + 7) b. 12(3 - |f) c. (0.4 + l.lc)3 d. (2y - l)(-y)

R e c a ll t h a t a f r a c t io n b a r m a y a c t as a g r o u p in g s y m b o l. A f r a c t io n b a r i n d ic a t e s

division. Any fraction | can also be w ritten as a • |. Y o u c a n u s e t h is fa c t a n d the

D is t r ib u t iv e P r o p e r t y t o r e w r it e s o m e f r a c t io n s as s u m s o r d iffe r e n c e s.

Pr o b l em 2 Rewriting Fraction Expressions

'iv 2

What sum or difference is equivalent to —g—?

7x£ 2 = | ( 7 x + 2 ) W rite division as m ultiplication.

= | ( 7 x ) + | ( 2 ) Distributive Property

= \x + | Simplify.

^ G o t It? 2. W h a t s u m o r d if f e r e n c e is e q u iv a le n t t o e a c h e x p re s s io n?

a. -_ 4 x — 16 3 — i_ 11 + 3 x b. — g— _ 15 + c. -j 26 —x dj 4 — 2x. — 3 —

T h e M u l t i p l ic a t i o n P r o p e r t y o f - 1 s ta te s t h a t - 1 • x = - x. T o s im p li f y a n e x p r e s s io n

such as - ( x + 6 ), y o u c a n re w rite th e e x p re s s io n as — l ( x + 6 ).

Using the M ultiplication Property of - 1

M ult iple Choice What is the simplified form of - (2y - 3x)?

GD 2y + 3x CJD -2y + (—3x) C O -2 y + 3x CO 2y - 3x

-(2y - 3x) = - l( 2 y - 3x) Multiplication Property of -1

= (-l)(2y) + (-l)(-3 x ) Distributive Property

= - 2 y + 3 x Simplify.

The correct choice is C.

^ G o t It? 3. W h a t is t h e s i m p li f i e d f o r m o f e a c h e x p re s s io n?

a. -(a + 5) b. -(-x + 31) c. — ( 4 x — 1 2 ) d. -(6 m - 9n)

c

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