Question 4
Expand and simplify:
I
II
III
(a)
(a + 1)2
(a)
(u - 5)2
(a)
(2 - x)2
(b)
(2x + 1)2
(b)
(3a - 1)2
(b)
(-2u - 3)2
(c)
(3a + 2b)2
(c)
(2x - 3y)2
(c)
-(5a - 3b)2
(d)
(u2 + 1)2
(d)
(uv + 2)2
(d)
(x2 - x)2
(e)
(e)
(e)
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Preliminary Mathematics Worksheet © Mathematics Plus, 2002 |
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Point your mouse to check your answers
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Question 1 |
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Simplify by collecting like terms: |
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I |
II |
III |
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(a) |
2a + 3a + 4a |
(a) |
3u + 4u - 6u |
(a) |
5x - 3x - 5x |
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(b) |
3x + 5x + 2y |
(b) |
a + b + 4a |
(b) |
u - 3 + 3u |
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(c) |
-3a + 2b + 4a + b |
(c) |
2x - x - 3y - y |
(c) |
8 + a - 2a |
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(d) |
5u2 + u + 2u - 2u2 |
(d) |
-u2 + v2 + 2u2 |
(d) |
-3x2 + x - 2x2 - 2x |
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(e) |
4xy + 3xy + y |
(e) |
6 - 2ab + ab |
(e) |
uv + vu + u + v |
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(f) |
a2 + a3 + 3a2 |
(f) |
2xy2 + x2y - xy2 |
(f) |
3ab2 - 2a2b - 6ab2 - 2a2b |
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Question 2 |
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Remove grouping symbols and simplify: |
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I |
II |
III |
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(a) |
3 + 2(a + 1) |
(a) |
-2u + 3(u - 1) |
(a) |
7(x + 2) + 2(x - 1) |
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(b) |
12 - (x - 1) |
(b) |
2(3a - 1) - 2a |
(b) |
5(u - 2) - (1 - 3u) |
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(c) |
a(a + 2) - 2(a + 2) |
(c) |
3x(x + 1) + 5(x + 1) |
(c) |
a(a + 3) - a(3 - a) |
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(d) |
u + v - (u - v) |
(d) |
u(u + v) - v(u - v) |
(d) |
x(3y + 2) - y(2x - 9) |
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(e) |
3x(2 + x) - x(x - 3) |
(e) |
5a(a + b) + 2a(a - b) |
(e) |
3u(u2+v) - 2u(u2 - v) |
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(f) |
ab(a+1) - ab(2a-1) |
(f) |
2xy(x+y) - xy(2x- y) |
(f) |
ab(2a+1) - a(ab- b) |
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Question 3 |
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Expand and simplify: |
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I |
II |
III |
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(a) |
(a + 1)(a+ 2) |
(a) |
(u + 1)(u - 3) |
(a) |
(x - 2)(x - 5) |
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(b) |
(2x + 1)(x + 1) |
(b) |
(a - 1)(3a + 2) |
(b) |
(u - 2)(3u - 1) |
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(c) |
(3a + 2)(2a + 1) |
(c) |
(2x + 1)(5x - 1) |
(c) |
(5a - 3)(2a - 5) |
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(d) |
(3 + u)(2 + u) |
(d) |
(u + 3)(4 - u) |
(d) |
(2 - 3y)(2y - 9) |
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(e) |
(2 + 5y)(y + 3) |
(e) |
(a - b)(2a + b) |
(e) |
(u - v)(u - 3v) |
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(f) |
(-a + 1)(2a+ 1) |
(f) |
(y - x)(7x - y) |
(f) |
-(-2b + 1)(-b + 3) |
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Question 4 |
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Expand and simplify: |
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I |
II |
III |
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(a) |
(a + 1)2 |
(a) |
(u - 5)2 |
(a) |
(2 - x)2 |
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(b) |
(2x + 1)2 |
(b) |
(3a - 1)2 |
(b) |
(-2u - 3)2 |
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(c) |
(3a + 2b)2 |
(c) |
(2x - 3y)2 |
(c) |
-(5a - 3b)2 |
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(d) |
(u2 + 1)2 |
(d) |
(uv + 2)2 |
(d) |
(x2 - x)2 |
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(e) |
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(e) |
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(e) |
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Question 5 |
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Expand and simplify: |
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I |
II |
III |
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(a) |
(x + 2)(x - 2) |
(a) |
(3 + a)(3 - a) |
(a) |
(2u + 3)(2u - 3) |
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(b) |
(4 - 3b) (4 + 3b) |
(b) |
(x - 2y) (x + 2y) |
(b) |
(4a + 5b)(4a - 5b) |
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(c) |
(a2 + 3)(a2 - 3) |
(c) |
(3x2 - 2) (3x2 + 2) |
(c) |
(a3 + 3b)(a3 - 3b) |
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(d) |
(uv + 1)(uv - 1) |
(d) |
(2uv + 1)(2uv - 1) |
(d) |
(x2y + 2)(x2y - 2) |
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(e) |
(3x2 + 2y2) (3x2 - 2y2) |
(e) |
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(e) |
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Question 6 |
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Expand and simplify (leave your answer in expanded form): |
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I |
II |
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(a) |
(x + 1)2 - x2 |
(a) |
(x + h)2 - x2 |
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(b) |
(a + 1)2 - 2a + 1 |
(b) |
(x + 1)2 - 2(x + 1) |
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(c) |
(x + 2)(x - 1) + (x + 2)2 |
(c) |
2a(a2 + 2a - 3) - (a + 2)2 |
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(d) |
(x + 3)2 + (x - 4)2 |
(d) |
(2x - 1)2 - (x - 3)2 |
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(e) |
2x - (1 - x)2 |
(e) |
(3x - 2)2 - 2(x - 3)2 |
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(f) |
(u + 2)2 - (u + 2)(u - 2) |
(f) |
(a + b)2 - (a + b)(a - b) |
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(g) |
(u + 3)2 - (u - 3)2 |
(g) |
(a + b)2 - (a - b)2 |
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