<< Chapter < Page Chapter >> Page >

4 x + 9 ( x 2 6 x 2 ) + 5 Remove parentheses . 4 x + 9 x 2 54 x 18 + 5 Combine like terms . 50 x + 9 x 2 13

By convention, the terms in an expression are placed in descending order with the highest degree term appearing first. Numerical terms are placed at the right end of the expression. The commutative property of addition allows us to change the order of the terms.

9 x 2 50 x 13

Got questions? Get instant answers now!

2 + 2 [ 5 + 4 ( 1 + a ) ]
Eliminate the innermost set of parentheses first.

2 + 2 [ 5 + 4 + 4 a ]

By the order of operations, simplify inside the parentheses before multiplying (by the 2).

2 + 2 [ 9 + 4 a ] Remove this set of parentheses . 2 + 18 + 8 a Combine like terms . 20 + 8 a Write in descending order . 8 a + 20

Got questions? Get instant answers now!

x ( x 3 ) + 6 x ( 2 x + 3 )
Use the rule for multiplying powers with the same base.

x 2 3 x + 12 x 2 + 18 x Combine like terms . 13 x 2 + 15 x

Got questions? Get instant answers now!

Practice set c

Simplify each of the following expressions by using the distributive property and combining like terms.

4 ( x + 6 ) + 3 ( 2 + x + 3 x 2 ) 2 x 2

7 x 2 + 7 x + 30

Got questions? Get instant answers now!

7 ( x + x 3 ) 4 x 3 x + 1 + 4 ( x 2 2 x 3 + 7 )

5 x 3 + 4 x 2 + 6 x + 29

Got questions? Get instant answers now!

5 ( a + 2 ) + 6 a 7 + ( 8 + 4 ) ( a + 3 a + 2 )

59 a + 27

Got questions? Get instant answers now!

x ( x + 3 ) + 4 x 2 + 2 x

5 x 2 + 5 x

Got questions? Get instant answers now!

a 3 ( a 2 + a + 5 ) + a ( a 4 + 3 a 2 + 4 ) + 1

2 a 5 + a 4 + 8 a 3 + 4 a + 1

Got questions? Get instant answers now!

2 [ 8 3 ( x 3 ) ]

6 x + 34

Got questions? Get instant answers now!

x 2 + 3 x + 7 [ x + 4 x 2 + 3 ( x + x 2 ) ]

50 x 2 + 31 x

Got questions? Get instant answers now!

Exercises

For the following problems, simplify each of the algebraic expressions.

h 3 h 5 h

7 h

Got questions? Get instant answers now!

3 a 2 + 6 a 2 + 2 a 2

11 a 2

Got questions? Get instant answers now!

14 a 2 b + 4 a 2 b + 19 a 2 b

Got questions? Get instant answers now!

210 a b 4 + 412 a b 4 + 100 a 4 b ( Look closely at the exponents. )

622 a b 4 + 100 a 4 b

Got questions? Get instant answers now!

5 x 2 y 0 + 3 x 2 y + 2 x 2 y + 1 , y 0 ( Look closely at the exponents. )

Got questions? Get instant answers now!

8 w 2 12 w 2 3 w 2

7 w 2

Got questions? Get instant answers now!

6 x y 3 x y + 7 x y 18 x y

Got questions? Get instant answers now!

7 x 3 2 x 2 10 x + 1 5 x 2 3 x 3 12 + x

4 x 3 7 x 2 9 x 11

Got questions? Get instant answers now!

21 y 15 x + 40 x y 6 11 y + 7 12 x x y

Got questions? Get instant answers now!

1 x + 1 y 1 x 1 y + x y

x y

Got questions? Get instant answers now!

5 x 2 3 x 7 + 2 x 2 x

Got questions? Get instant answers now!

2 z 3 + 15 z + 4 z 3 + z 2 6 z 2 + z

2 z 3 5 z 2 + 16 z

Got questions? Get instant answers now!

18 x 2 y 14 x 2 y 20 x 2 y

Got questions? Get instant answers now!

9 w 5 9 w 4 9 w 5 + 10 w 4

18 w 5 + w 4

Got questions? Get instant answers now!

2 x 4 + 4 x 3 8 x 2 + 12 x 1 7 x 3 1 x 4 6 x + 2

Got questions? Get instant answers now!

17 d 3 r + 3 d 3 r 5 d 3 r + 6 d 2 r + d 3 r 30 d 2 r + 3 7 + 2

16 d 3 r 24 d 2 r 2

Got questions? Get instant answers now!

a 0 + 2 a 0 4 a 0 , a 0

Got questions? Get instant answers now!

4 x 0 + 3 x 0 5 x 0 + 7 x 0 x 0 , x 0

8

Got questions? Get instant answers now!

2 a 3 b 2 c + 3 a 2 b 2 c 0 + 4 a 2 b 2 a 3 b 2 c , c 0

Got questions? Get instant answers now!

6 x 3 + 12 x + 5

6 x 3 + 12 x + 5

Got questions? Get instant answers now!

7 ( a + 2 ) + 4

7 a + 18

Got questions? Get instant answers now!

2 b + 6 ( 3 5 b )

28 b + 18

Got questions? Get instant answers now!

5 a 7 c + 3 ( a c )

Got questions? Get instant answers now!

8 x 3 x + 4 ( 2 x + 5 ) + 3 ( 6 x 4 )

31 x + 8

Got questions? Get instant answers now!

2 z + 4 a b + 5 z a b + 12 ( 1 a b z )

Got questions? Get instant answers now!

( a + 5 ) 4 + 6 a 20

10 a

Got questions? Get instant answers now!

( 4 a + 5 b 2 ) 3 + 3 ( 4 a + 5 b 2 )

Got questions? Get instant answers now!

( 10 x + 3 y 2 ) 4 + 4 ( 10 x + 3 y 2 )

80 x + 24 y 2

Got questions? Get instant answers now!

1 ( 3 x + 15 ) + 2 x 12

5 x + 3

Got questions? Get instant answers now!

1 ( 2 + 9 a + 4 a 2 ) + a 2 11 a

Got questions? Get instant answers now!

1 ( 2 x 6 b + 6 a 2 b + 8 b 2 ) + 1 ( 5 x + 2 b 3 a 2 b )

3 a 2 b + 8 b 2 4 b + 7 x

Got questions? Get instant answers now!

After observing the following problems, can you make a conjecture about 1 ( a + b ) ?
1 ( a + b ) =

Got questions? Get instant answers now!

Using the result of problem 52, is it correct to write
( a + b ) = a + b ?

yes

Got questions? Get instant answers now!

3 ( 2 a + 2 a 2 ) + 8 ( 3 a + 3 a 2 )

Got questions? Get instant answers now!

x ( x + 2 ) + 2 ( x 2 + 3 x 4 )

3 x 2 + 8 x 8

Got questions? Get instant answers now!

A ( A + 7 ) + 4 ( A 2 + 3 a + 1 )

Got questions? Get instant answers now!

b ( 2 b 3 + 5 b 2 + b + 6 ) 6 b 2 4 b + 2

2 b 4 + 5 b 3 5 b 2 + 2 b + 2

Got questions? Get instant answers now!

x 3 x ( x 2 7 x 1 )

3 x 3 + 21 x 2 + 4 x

Got questions? Get instant answers now!

a b ( a 5 ) 4 a 2 b + 2 a b 2

Got questions? Get instant answers now!

x y ( 3 x y + 2 x 5 y ) 2 x 2 y 2 5 x 2 y + 4 x y 2

x 2 y 2 3 x 2 y x y 2

Got questions? Get instant answers now!

3 h [ 2 h + 5 ( h + 2 ) ]

Got questions? Get instant answers now!

2 k [ 5 k + 3 ( 1 + 7 k ) ]

52 k 2 + 6 k

Got questions? Get instant answers now!

8 a [ 2 a 4 a b + 9 ( a 5 a b ) ]

Got questions? Get instant answers now!

6 { m + 5 n [ n + 3 ( n 1 ) ] + 2 n 2 } 4 n 2 9 m

128 n 2 90 n 3 m

Got questions? Get instant answers now!

5 [ 4 ( r 2 s ) 3 r 5 s ] + 12 s

Got questions? Get instant answers now!

8 { 9 [ b 2 a + 6 c ( c + 4 ) 4 c 2 ] + 4 a + b } 3 b

144 c 2 112 a + 77 b + 1728 c

Got questions? Get instant answers now!

5 [ 4 ( 6 x 3 ) + x ] 2 x 25 x + 4

Got questions? Get instant answers now!

3 x y 2 ( 4 x y + 5 y ) + 2 x y 3 + 6 x 2 y 3 + 4 y 3 12 x y 3

18 x 2 y 3 + 5 x y 3 + 4 y 3

Got questions? Get instant answers now!

9 a 3 b 7 ( a 3 b 5 2 a 2 b 2 + 6 ) 2 a ( a 2 b 7 5 a 5 b 12 + 3 a 4 b 9 ) a 3 b 7

Got questions? Get instant answers now!

8 ( 3 a + 2 )

24 a 16

Got questions? Get instant answers now!

4 x y 2 [ 7 x y 6 ( 5 x y 2 ) + 3 ( x y + 1 ) + 1 ]

24 x 2 y 4 16 x 2 y 3 + 104 x y 2

Got questions? Get instant answers now!

Exercises for review

( [link] ) Simplify ( x 10 y 8 z 2 x 2 y 6 ) 3 .

Got questions? Get instant answers now!

( [link] ) Find the value of 3 ( 4 9 ) 6 ( 3 ) 1 2 3 .

4

Got questions? Get instant answers now!

( [link] ) Write the expression 42 x 2 y 5 z 3 21 x 4 y 7 so that no denominator appears.

Got questions? Get instant answers now!

( [link] ) How many ( 2 a + 5 ) ' s are there in 3 x ( 2 a + 5 ) ?

3 x

Got questions? Get instant answers now!

( [link] ) Simplify 3 ( 5 n + 6 m 2 ) 2 ( 3 n + 4 m 2 ) .

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask