Worksheet :
Expanding, Factoring and Solving Systems of Linear Equations.
1. Expand and Simplify
a. 4(3x + 2y)(x – 3y)
b. (x + 3y – 2)(x + 4y +3)
c. (9x – 3y)(2x-y) + 4y2
d. (3x – 2y)(x + 3y)(2x – y)
e. (2x + 4)(x – 1) + x(2 + x)
f. -7(x + 2y)(y – 2x)
2. Expand and Simplify using Pascal’s triangle.
a. (a – b)4
b. (2a – b)5
c. (2a + 3b)3
3. Factor:
a.
b.
c.
d.
e.
36p2 – 49
x2 + 7x + 10
2x2 – 50
35x2 + 5x – 40
1 x2 – 1 y2
4
f.
g.
h.
i.
j.
k.
l.
m.
9
–1
(a – 2)(a + 2) + (a – 2)(a – 2)
r(p2 + 5) – s(p2 + 5)
x3 + 3x2 – 10x
(x + 3)2 – y2
81x2 – 4
x2 + 2x – 15
6x2 + 19x + 3
x4
n.
o.
p.
q.
r.
s.
t.
u.
v.
w.
x.
y.
z.
x2 + 5x + 6
(x – 2)2 – 25
27b2 – 12g2
4m2 – 17m + 18
x2 – 9
x2 – 49
3m2 – m – 30
10x2 – 19x – 4
9x2 + 15x + 4
x2 – x – 30
2x2 – 21x + 40
8m2 – 5m – 3
14m2 + 17m – 22
4. Solve for x and y using the substitution method
a. y = 2x
x + y = 12
c. x – y = 2
4x – 3y = 11
e. 6x – y = -4
2x + 2y = 15
b. x = 3y – 1
x + 2y = 9
d. -2x + 3y = 14
x + 2y = 7
f. y = 1 x – 3
2
y= 3x–1
2
5. Solve for x and y using the elimination method
a. 15x – 2y = 4
x + 2y = 8
c. 6x – 2y = 10
x – 2y = -5
e. 7x – 4y = -10
4y = x – 2
b. -3x + 2y = 11
3x – 4y = -19
d. 5x + y = 2
5x – 3y = 14
f. y = 2 x – 1
3
y = -x + 4
6. Solve each word problem by writing the problem as a system of linear
equations.
a. The second of two numbers is 5 more than twice the first. The sum of the
numbers is 44. Find the numbers.
b. For a play, Sandy sold 6 adult tickets and 15 student tickets, and collected
$48. Kyle sold 8 adult tickets and 7 student tickets, and collected $38.
Find the cost of adult tickets, and of student tickets.
c. The coin box of a vending machine contains $6.20 in dimes and quarters.
There are 32 coins in all. How many of each kind are there?