EXPANDING BRACKETS
Higher Tier
EXPANDING BRACKETS LIKE 3(X + 2)
MULTIPLYING OR EXPANDING BRACKETS

The number or letter outside the bracket is multiplied by every separate term inside the
bracket.
The “Rectangle Method” can also
be used.
Examples
1.
3(x + 9) = 3x + 27
2.
4(x  3) = 4x  12
3.
3(4 + x) = 12  3x
4.
5(x  2) = 5x + 10
5.
a(a + 3) = a² + 3a
6.
2x(x  1) = 2x²  2x
7.
3x(4  x) = 12x + 3x²
8.
r(2r + h) = 2r² + rh
9.
½ w(2 + 4r) = w + 2wr
10.
Expand and Simplify 3(x  9) + 2(x + 8)
[be careful with the signs]
3(x  9) + 2(x + 8) = 3x  27 + 2x + 16
= 5x  11
expandingbrackets
Multiply out the brackets
Collect like terms
©RSH 26-Mar-10
Page 1 of 4
EXPANDING BRACKETS
Higher Tier
EXERCISE 1
1.
2.
3.
4.
Multiply out
a.
5(x + 3)
h.
2(1 - 3n)
b.
3(n - 4)
i.
n(5 + 3n)
c.
2(5 + 3n)
j.
x(2x + 3)
d.
4(3 - 2a)
k.
x(3 - 2x)
e.
4(2x - 7)
l.
a(a - 5)
f.
5(3p + 1)
m.
2a(3 - a)
g.
6(3 - 4n)
n.
4n(2n + 3)
Expand
a.
-3(n + 2)
g.
-2p(p + 2)
b.
-2(3 + 4a)
h.
-3a(2a + 5)
c.
-4(2n -1)
i.
-3x(4 - x)
d.
-5(3 - 4x)
j.
-2n(3 - n)
e.
-6(3x + 5)
k.
-3q(2q - 5)
f.
-5(4 - 5x)
Multiply out
a.
4(x + b)
h.
-2x(3a + x)
b.
3(x - a)
i.
-4x(x - a)
c.
x(n - 2a)
j.
-2a(3n - 4x)
d.
n(4a + n)
k.
pq(p + q)
e.
3a(4 - 5x)
l.
pr(r + 2h)
f.
2n(3 - 4a)
m.
ab(h - a)
g.
5n(3a - 2n)
n.
rs(s - r)
Expand and simplify
a.
4 + 3(2n + 3)
h.
3(x + 4) + 2(3 + 2x)
b.
n - 5 + 2(3 - 2n)
i.
5(2a -1) - 3(1 - 2a)
c.
3n² + n(3 + 2n)
j.
5n(n - 2) + 2n(1 - 2n)
d.
2n(3 - n) + 5n
k.
x(3 + 4x) + 2x(x - 2)
e.
x(2x + 5) – x
l.
x(2 + x) - 2(2 - x)
f.
2a(4 - a) + 5 + 6a
m.
5(2 - n) + 2n(n + 3)
g.
3(2n + 5) - 6 – n
n.
2x(2x - 3) - 3(4 – x)
expandingbrackets
©RSH 26-Mar-10
Page 2 of 4
EXPANDING BRACKETS
Higher Tier
EXPANDING BRACKETS LIKE (X + 2)(X + 4)
MULTIPLICATION OF TWO BRACKETS

Each term in the first bracket is multiplied with each term in the second bracket. The
expansion is then simplified.

Be careful with signs!
Examples
Expand and simplify
1.
(x + 2)(x + 5)
= x² + 5x + 2x + 10
= x² + 7x + 10
2.
(2x  3)(x + 1)
= 2x² + 2x  3x  3
= 2x²  x  3
3.
(x + y)²
= (x + y)(x + y)
= x² + xy + yx + y²
= x² + 2xy + y²
4.
(a + b)(2 + c)
= 2a + ac + 2b + bc
5.
(x  2)(x  4)
= x²  4x  2x + 8
[remember that xy = yx]
= x²  6x + 8
expandingbrackets
©RSH 26-Mar-10
Page 3 of 4
EXPANDING BRACKETS
Higher Tier
EXERCISE 2
EXPAND AND SIMPLIFY
1.
(x + 1)(x + 2)
2.
(x + 2)(x + 4)
3.
(x + 8)(x + 3)
4.
(x + 4)(x + 5)
5.
(x + 3)(x + 12)
6.
(x - 1)(x - 2)
7.
(x - 3)(x - 4)
8.
(x - 2)(x - 8)
9.
(x - 10)(x - 2)
10.
(x - 5)(x - 2)
11.
(x - 1)(x + 2)
12.
(x - 4)(x + 5)
13.
(x - 3)(x + 1)
14.
(x - 7)(x + 4)
15.
(x - 5)(x + 5)
16.
(x + 1)(x - 2)
17.
(x + 5)(x - 7)
18.
(x + 10)(x - 2)
19.
(x + 10)(x - 3)
20.
(x + 5)(x - 2)
21.
(x + 3)(x - 4)
22.
(2x + 1)(3x + 2)
23.
(2x + 3)(2x + 4)
24.
(3x + 8)(2x + 3)
25.
(4x + 4)(3x + 6)
26.
(2x + 3)(5x + 12)
27.
(2x - 7)(2x + 10)
28.
(4x + 2)(2x - 1)
29.
(3x - 5)(4x + 4)
30.
(2x + 9)(4x - 2)
31.
(5x - 8)(3x + 4)
32.
(2x + 3)(3x - 3)
expandingbrackets
©RSH 26-Mar-10
Page 4 of 4