Math 10
Simplifying Expressions (Part 1)
* A term is a collection of numbers and/or letters which are multiplied together.
* Every term has a number part – the coefficient
* The letter part is called the variable
*Terms can only be added or subtracted if their variables are like terms.
1. Simplify each of the following expressions by combining like terms:
(a) 5x  3x  7 x
(b) 7 y  3 y  5 y
(c) 2x  3x  5x
(d) 3ab  2ab  7ab
(e) 2x  5  3x  6
(f) 6 x  2  (3x)  7
(g)  z  ( z )  6
(h) x  x  5
(i) 2 x  ( x)  5
(j) a 2  a 3  a 2  6a
(k) a 2b  a 2b 2
(l) 3 x  5 y  3 y  3
(m) 7 xy  3x 2 y  6 xy2
(n)  2m  (2n)  2mn
(o) mn  7mn
(p) 4m  4
(q) 3a 2  3a  6a  7a 2
(r) 4a  (4a )  4ab
(s) 2m  4m  (6m)  4m
(t)  5a  3b  a  b
2. Simplify each of the following expressions:
(a) 8x  5x  3x
(b)  3 y  2 y  8 y
(c) 4a  (2a )  5a
(d)  2m  mn  m
(e) ab  3ab  (2a)  (4b)
(f) 3mn  2mn  (mn)
(g) 2a  3a 2  a  4a 2
(h) 5  2a  7  2a
(i) x 2  xy  y  2 xy
(k)  5m  (2n)  6m  (3n)
NAME:_____________
Math 10
Simplifying Expressions (Part 2)
NAME:_____________
* Sometimes an algebraic expression needs to be expanded first before it can be simplified.
* The coefficient outside the brackets multiplies every term inside the brackets.
* For example, 4( x  2)  4 x  8
Simplify each of the following algebraic expressions by expanding then combining like terms.
1. 3( x  2)  5( x  3)
2. 5( x  1)  7( x  4)
3.  2(a  4)  3(a  2)
4.  7(a  1)  9(a  4)
5. 3(n 2  1)  8(n 2  1)
6. 4(n 2  3)  (n 2  7)
7.  6( x  5)  ( x  2)
8. 3( x  y )  2( x  y )
9. 5(2 x  1)  4(3x  2)
10. 5(3x  1)  6(2 x  3)
11. 3(2 x  5)  4(5 x  2)
12. 3(2 x  3)  7(3x  1)
13.  2(n  4)  4(2n  1)
14.  4(n  3)  (2n  7)
15. 3(2 x  4 y )  2( x  9 y )
16.  7(2 x  3 y )  9(3x  y )
17. Simplify by expanding and collecting like terms and then evaluate the following expressions if:
x = -15
y = -10
w = -5
SHOW ALL WORK!
(a) 9(2 x  4)  2(7 x  12)
(d)
 3 y  16  2w
2(6 x  3 y )
(b) 5(3 y  1)  (6  5 y )
(e)
(c) (9w  5)  8( y  2)
2(4 y  11)
5(3w  2 y )
(f)
 6 yw
3x
18. Substitute, then evaluate. By placing the variable above its corresponding value, decode the message.
(a)
7  2a
; a = -1
5
(b)  2o  5  0.5o ; o = 18
(c)
3i  3  6i
;I=6
3
(d)
4h
6
 3h  ; h = 3
2
h
(e) 2.1 f  8.2 f ; f = 0.1
(f)
16
 5t ; t = -0.4
t
(h) 2r  5  3r  6  10r ; r = (-1)2
(i) 16  3g  8  7 g  1; g = -(1)2
(g)  5m  3  m ; m = 0.2
-3.8
1
-38
-1
-3
-22
1.03
-22
20
19
-38