Algebraic Manipulation – Expanding, Factorising
Maths
high_school
10 questions
~20 mins
0 views0 downloads
About This Worksheet
A comprehensive Maths worksheet on Algebraic Manipulation – Expanding, Factorising for high school students. Includes a variety of question types including multiple choice, short answer, and true/false questions.
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Algebraic Manipulation – Expanding, Factorising
Subject: MathsGrade: high_school
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Algebraic Manipulation – Expanding, Factorising
Maths
Instructions: Read each question carefully and provide your answers in the space provided. For multiple choice questions, circle the correct option. For short answer questions, write your complete answer. For true/false questions, indicate whether the statement is true or false.
A
Multiple Choice Questions
Select the correct answer for each question.
1.
What is the result of expanding (x + 3)(x - 2)?
AA) x^2 + x - 6
BB) x^2 + x + 6
CC) x^2 + 5x - 6
DD) x^2 - x - 6
2.
Which expression is equivalent to 3(x - 4) + 2(x + 1)?
AA) 5x - 10
BB) 5x - 10
CC) 5x - 10
DD) 5x - 10
3.
What is the factorization of x^2 - 9?
AA) (x - 3)(x + 3)
BB) (x - 9)(x + 1)
CC) (x + 3)(x + 3)
DD) (x - 3)^2
4.
What is the simplified form of (2x^2 + 6x)/(2x)?
AA) x + 3
BB) x + 3/2
CC) 2x + 6
DD) x + 2
5.
Complete the square for x^2 + 6x.
AA) (x + 3)^2 - 9
BB) (x + 6)^2 - 36
CC) (x - 3)^2 + 9
DD) (x - 6)^2 + 36
6.
What is the result of expanding (x - 5)^2?
AA) x^2 - 10x + 25
BB) x^2 + 10x + 25
CC) x^2 - 25
DD) x^2 - 5
7.
Factorise the expression 4x^2 - 25.
AA) (2x - 5)(2x + 5)
BB) (4x - 5)(4x + 5)
CC) (2x + 5)^2
DD) (2x - 5)^2
8.
What is the simplified form of (x^2 - 4)/(x - 2)?
AA) x + 2
BB) x - 2
CC) x^2 + 4
DD) x + 4
9.
Which expression represents the completed square form of x^2 - 8x + 15?
AA) (x - 4)^2 - 1
BB) (x - 4)^2 + 1
CC) (x - 8)^2 - 49
DD) (x - 2)^2 + 11
10.
What is the factorization of 2x^2 + 8x?
AA) 2x(x + 4)
BB) 2(x^2 + 8)
CC) (2x + 4)(x + 4)
DD) 2x(2x + 4)
B
True/False Questions
Circle True or False for each statement.
1.
The expression x^2 + 4 cannot be factored over the real numbers.
2.
Completing the square can help in solving quadratic equations.
3.
The expression (x - 1)(x + 1) equals x^2 - 1.
C
Short Answer Questions
Answer each question in the space provided.
1.
Expand the expression (x + 2)(x + 5).
2.
Factorise the expression x^2 + 10x + 21.
3.
Simplify the fraction (x^2 - 9)/(x - 3).
4.
Complete the square for x^2 - 6x.
5.
Expand and simplify (3x + 4)(2x - 5).
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- Created
- 4/14/2025
- Updated
- 12/29/2025
- Type
- worksheet