– ALGEBRAIC EXPRESSIONS –
Evaluate One Variable in Terms of Another
An equation that contains two variables can be written so that the value of one variable is given in terms of the
other. For instance, y = 3x + 3 is an equation with two variables, x and y, in which the value of one variable, y, is
written in terms of the other variable, x. The value of y is 3x + 3.
If 4a + 8b = 16, what is the value of a in terms of b?
Isolate a on one side of the equation. Subtract 8b from both sides: 4a = 16 – 8b. Now, divide both sides of the
equation by 4: a = 4 – 2b. The value of a in terms of b is 4 – 2b.
Practice
1. 9a + 12a2 – 5a =
a. 16a
b. 16a2
c. 12a2 – 4a
d. 12a2 + 4a
e. 26a2
2.
(3a)(4a)
6(6a2)
1
a. 3
2
b. a
1
c. 3a
1
d. 3a2
5. When x = 3, 2x2 – 5x + 3 =
a. –6
b. 0
c. 6
d. 33
e. 36
7a
6. When a = –2, a2 + a =
a. –14
b. –7
7
c. –4
7
d. 4
e. 7
=
e. 2
y2
y
7. When x = –2, x2 + –2x =
3.
(5a + 7b)b
(b + 2b)
=
a.
a. 4a
b. 4ab
c. 2a + 4b
5a + 7b
d. 3
e. 5a + 5b
b.
c.
d.
e.
3y
4
y3
4
(–y2 + y)
4
(y2 – y)
4
(y2 + y)
4
4p(p + r)
8. When p = 6, pr =
4. (2x2)(4y2) + 6x2y2 =
a. 12x2y2
b. 14x2y2
c. 2x2 + 4y2 + 6x2y2
d. 8x2 + y2 + 6x2y2
e. 8x4y4 + 6x2y2
a. 8
b. 24 + r
c. 24 + 3r
6
d. r
e.
15
24 + 4r
r
– ALGEBRAIC EXPRESSIONS –
9. When a = 3, (4a2)(3b3 + a) – b3 =
a. 72b3 + 108
b. 107b3 + 39
c. 107b3 + 108
d. 108b3 + 39
e. 216
14. If 7a + 20b = 28 – b, what is the value of a in
terms of b?
a. 4 – 3b
b. 4 + 3b
19
c. 4 – 7b
22
d. 4 – 7b
(cd)2
b+4
10. When c = 1 and d = 4, c+d =
a.
e. –3
16
5
x
15. If 4(y + 1) = 10, what is the value of y in terms
of x?
b. 4
c.
17
4
1
a. – 4x
d. 5
e.
1
b. 4x
25
4
4
c. 9x
6x2
2
d. 3x
4x
11. When x = 2 and y = 3, 2y2 + 3y =
a.
b.
c.
d.
e.
3
e. 2x
4
9
4
3
20
9
21
9
13
3
16. If fg + 2f – g = 2 – (f + g), what is the value of g in
terms of f ?
a. –1
1
b. f
a
b
12. When a = 1 and b = –1, ab + +
a. –4
b. –3
c. –2
d. –1
e. 0
a2
–
b2
c.
=
4
f
d. 2 – 2f
e.
2 – 3f
f
17. If a(3a) – b(4 + a) = –(a2 + ab), what is the value
of b in terms of a?
1
a. 2a
1
b. 2a2
c. 2a
d. a2
e. 4a2
3
13. If 2g = 9h – 15, what is the value of g in terms
of h?
1
5
a. 6h + 3
b. 6h – 15
c. 6h – 10
27
45
d. 2h – 2
e. 18h – 30
16
– ALGEBRAIC EXPRESSIONS –
10 (x2y)
18. If 4g2 – 1 = 16h2 – 1, what is the value of g in
terms of h?
a. h
b. 2h
c. 4h
d. h2
e. 4h2
20. If xy
= 5y, what is the value of y in terms of x?
2
a. x
b. 2x
c. 2x
d. 2x
x2
e. 2
19. If 8x2 – 4y2 + x2 = 0, what is the value of x in
terms of y?
2
a. 3y
3
b. 2y
4
c. 9y2
2
d. 3y2
3
e. 2y2
17