What terms can you
combine?
You can combine any
terms that have exactly
the same variables
with exactly the same
exponents.
A n a lg e b r a ic e x p r e s s io n i n s im p le s t f o r m h a s n o lik e t e r m s o r p a r e n th e s e s.Not Simplified Simplified
2(3x - 5 + 4x) 14x - 10
Y o u c a n u s e th e D is t r i b u t i v e P r o p e r t y t o h e lp c o m b in e lik e te r m s. T h in k o f th e
D is t r ib u t iv e P r o p e r t y as ba + ca = (b + c)a.Combining Like Terms
What is the simplified form of each expression?0 8 x 2 + 2 x 2
8 x 2 + 2x 2 = (8 + 2 )x 2 Distributive Property
= 10x 2 Simplify.0 5x - 3 - 3x + 6y + 4
5x - 3 - 3x + 6 y + 4 = 5x + (-3 ) + (-3 x ) + 6 y + 4
= 5 x + ( —3 x ) + 6 y + (-3 ) + 4
= (5 — 3)x + 6 y + (—3) + 4
= 2 x + 6 y + 1Rewrite as a sum.
Com m utative Property
Distributive Property
Simplify.© G o t It? 5. What is the simplified form of each expression in parts (a)-(c)?
a. 3y — y b. —7 m n 4 — 5 m n 4
d. Reasoning Can you sim plify 8 x 2 - 2x 4 - 2x + 2 + xy fu rth e r? E x p la in.c. 7y 3z - 6 yz 3 + y3zLesso n Ch eck
Do y o u k n o w H OW?
- 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? U s e
th e D is trib u tiv e P ro p e rty.
a. (;+ 2)7
b. — 8 (x — 3)
c. -(4 - c)
d. -(11 + 2b)
Rewrite each expression as a sum.
- 8 x 2 + 3xy - 9x - 3
- 2ab - 5ab2 - 9a2b
Tell whether the terms are like terms.- 3a and -5a 5. 2xy 2 a n d -x2y
_. MATHEMATICAL
Do yo u UN DERSTAN D? | g f PRACTICES
6. V o c a b u l a r y Does each equation demonstrate the
Distributive Property? Explain.
a. — 2 (x + 1 ) = — 2 x - 2
b. (s - 4)8 = 8 (s - 4)
c. 5n - 45 = 5{n - 9)
d. 8 + ( t + 6 ) = (8 + t) + 6- M ental M ath How can you express 499 to find the
product 499 X 5 u s in g m e n t a l m a th? E x p la in. - R e a s o n i n g Is e a c h e x p re s s io n in s im p lifie d fo rm?
Justify yo u r answer.
a. 4xy 3 + 5x3y
b. —(y — 1 )
c. 5x 2 + 12xy - 3yx