### A4 Factorising Algebraic Expressions (inc DOTS)

```The Oakwood Academy
Expressions (A4iii)
(Including Difference of Two Squares; Factorising
when coefficient of x2 >1)
Page 1
Q1.
Factorise
3x² + 14x + 8
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(Total 2 marks)
Q2.(a)
Factorise
3n2 + 7n + 4
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(2)
(b)
Hence, or otherwise, write 374 as the product of its prime factors.
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(2)
(Total 4 marks)
Page 2
Q3.(a)
Factorise
x + 10x + 24
2
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(2)
(b)
Hence or otherwise,
solve x2 + 10x + 24 = 0
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(1)
(Total 3 marks)
Q4.(a)
Expand and simplify
(2x + 1)(3x − 4)
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(2)
(b)
Factorise
6x2 − 23x − 4
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(2)
(Total 4 marks)
Page 3
Q5.(a)
Factorise
x −9
2
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(1)
(b)
Hence, simplify fully
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(3)
(Total 4 marks)
Q6.
Factorise
9a2 − b2
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(Total 2 marks)
Q7.(a)
Show clearly that
(x + 5)(x − 5) ≡ x − 25
2
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(1)
Page 4
(b)
Simplify
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(3)
(Total 4 marks)
Q8.
Simplify fully
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(Total 4 marks)
Page 5
5x2 + 14x − 24 = 0
Q9.Solve the equation
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(Total 3 marks)
Q10.
(a)
Factorise fully
2x² − 2x − 40
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(3)
(b)
Factorise fully
(x + y)² + (x + y)(2x + 5y)
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(3)
(Total 6 marks)
Page 6
Q11.Simplify
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(Total 3 marks)
Q12.
(a)
Factorise
3x − 13x − 10
2
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(2)
(b)
Simplify
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(2)
(Total 4 marks)
Page 7
Q13.Simplify
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(Total 3 marks)
Q14.
(a)
Factorise fully
3x² − 12
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(2)
(b)
Factorise
5x² + 4xy − 12y²
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(3)
(Total 5 marks)
Page 8
Q15.
(a)
Factorise fully
12c²d − 9d²
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(2)
(b)
Factorise fully
(w + 4)³ − (w + 4)²(w + 1)
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(3)
(Total 5 marks)
Q16.
(a)
Factorise fully
5m² − 20p²
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(3)
Page 9
(b)
You are given that
p = 15
and
5m² − 20p² = 0
Using your answer to part (a), or otherwise, work out the values of m.
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(2)
(Total 5 marks)
Page 10
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