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
0
