Basic Mathematics for College Students

Chapter 8 Summary and Review 699

The distributive propertycan be used to
remove parentheses:

a(bcd)abacad

a(bc)abac a(bc)abac

Multiply:

Multiply:

0.8mn1.4

0.2(4m 5 n7)0.2(4m)(0.2)(5n)(0.2)(7)

 7 x 21

7 (x3) 7 x 7  3

Like termsare terms with exactly the same
variables raised to exactly the same powers.

and are like terms.

and are unlike terms because the variable has different

exponents.

and are unlike terms because they have different

variables.

0.5xyz 3.7xy

 4 t^33 t^2 t

3 x  5 x

Simplifying the sum or difference of like terms
is calledcombining like terms.Like terms can
be combined by adding or subtracting the
coefficients of the terms and keeping the same
variables with the same exponents.

Simplify: Think:.

Simplify: Think:

and.

Simplify:

k 8

2(k1)3(k2) 2 k 2  3 k 6

(19)p 8 p

5 p^2 pp^2  9 p 4 p^2  8 p (51)p^2  4 p^2

4 a 2 a 6 a (42)a 6 a

Simplify each expression.

15. 
    
    
    
    16. 
        
    
    
    
    

17 18.

Use the distributive property to remove parentheses.

19. 
    
    
    
    20. 
        
    
    
    
    


20. 
    
    
    
    22. 
        
    
    
    
    

List the like terms in each expression.

23. 
    
    
    
    24. 
        
    
    
    
    

Simplify each expression by combining like terms, if possible.

25. 
    
    
    
    26. 
        
    
    
    
    


26. 
    
    
    
    28. 
        
    
    
    
    


27. 55.7k^2 55.6k^2

nnnn 5(p2)2(3p4)

8 p 5 p 4 p  5 m 2  2 m 2

7 a 3  9 a 2 x^2  2 x 3 x^2 x

2(3c7)(2.1)

3

4

(4c8)

5(x3) (2x 3 y)

7

2



2

7

0.4(5.2ƒ) r

4(7w) 3( 2 x)(4)

30.

31. 
    
    
    
    32. 
        
    
    
    
    


32. 
    
    
    
    34. 
        
    
    
    
    


33. Write an equivalent expression for the given
    expression using fewer symbols.
    a. b.
    c. d.


34. GEOMETRY Write an algebraic expression in
    simplified form that represents the perimeter of the
    triangle.

4 x(1) 4 x(1)

1 x  1 x

36 a

1

9

h

3

4

b 36 a

1

3

b

3

5

wa

2

5

wb

10 x 10 y 4 x^3  4 x^2  4 x 4

8 a^3  4 a^3  2 a 4 a^3  2 a 1

REVIEW EXERCISES

 

   

 

 

  

(x + 7) ft

(2x – 3) ft

x ft