Algebra P3
7-#5: Exponents, and Distributive, and Like Terms
Name: ______________________________
Period: _____ 11/21-22/13
Use the Distributive Property to simplify each expression. You may need to use some exponent properties.
1) 3( x  2)
2) 3x( x  2)
3) 3x 2 ( x  2)
4) 3x3 ( x  2)
5) 5( x 2  3x  7)
6) 5x 4 ( x 2  3x  7)
Like Terms are terms that have the same exact
variable part (including exponents) as each other.
Like Terms
Not Like Terms
x and x
x and y
2xy and 8xy
2xy
and
8) 5x 2 y  2 x 2  4 y 2 
7) x2 ( x3  3x5  y 2 )
Combine Like Terms by combining their
coefficients and leaving the variable parts
(including exponents) unchanged.
8x
Simplify
Cannot be Simplified
x  x  2x
x y
2xy  (8xy)  6 xy
2xy  (8 x)
5a 2 and 3a 2
2x and 2x 2
5a 2  3a 2  8a 2
2x  2x 2
3xy 2 and 4xy 2
3xy 2 and 4x 2 y
3xy 2  4 xy 2  1xy 2
3xy 2  4x 2 y
Simplify by combining like terms.
10) 9 xy  4 xy
9) 3x2  5x2
11) x  x  x2  3x2
12) 3x2  2 x2  4 x  8x  5  8
Possible Answers: 2 x  4 x , 5 xy, 8 x , 4 x  3x, x  4 x  13, x  12 x  3
2
2
2
2
2
Distribute and Combine Like Terms:
13) 3x( x 2  4 x)  5( x3  2 x 2 )
14) 5(2 x2  3x  4)  x(2 x  5)
15) 3xy(2 x  8)  2 y  4 x  7 x 2 
16) 5x2 ( x3  4 x2 )  x( x 4  x3 )
17) 5x2  3x( x  7)  4 x
18) 4 x2 (3x  5)  2 x(5x  10)
Possible Answers: 12 x 2  20 x  20, 2 x 2  25x, 20 x 2 y  16 xy,
14 x y  15x, 8x  22 x , 12 x  10 x  20 x, 6 x  19 x
2
3
2
3
2
5
4
The Point-Slope Form of a line is given each problem below. Determine the slope and point for each.
Recall: y  y1  m  x  x1  . Example: y  3  4( x  1) m = 4, point: (1, –3)
19) y  4  2( x  5)
m  ___ point = (
20) y  2 
,
)
3
( x  5)
4
m  ___ point = (
*check this one with your teacher or a friend to make sure
you have it right.
21) y  3 
,
1
( x  2)
2
m  ___ point = (
)
Plot the given point and then from that point, plot the given slope.
1
23) m   2 point:  4, 5
22) m 
point:  3, 2 
y
4
24) m 
y
,
)
5
point:  1, 4 
3
y
x
x
x
Write the equation of the line in
Point-Slope Form:
Write the equation of the line in
Point-Slope Form:
___________________________
Write the equation of the line in
Point-Slope Form:
___________________________
___________________________
Graph the line given in Point-Slope Form. Do not change the form of the equation.
1
1
y  2  1 x  4 
27)
25)
26)
y  3   x  1
y  2    x  4
2
3
, )
m  ___ point = (
, )
, )
m  ___ point = (
m  ___ point = (
y
y
x
y
x
x