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mathematics UK Year 10 Mathematics (KS4)
 
Solved problems for the chapter:
 

Factorising algebraic expressions

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:factorising_algebraic_expressions/5382/


Example 1.

Factorise using the difference of cubes identity:


    
Example 2.

Present the common factor and decompose the expression:


    
3.
Find all divisors of the given expression:

    
4.
Find all divisors of the given expression:

    
5.

Disassemble two binomials into a product:

   
6.
Find all divisors of the given expression:

    
7.

Write the expression as the sum of a perfect square and an integer. For which p expression takes the smallest value and what is this minimum value?

    
8.
Find all divisors of the given expression:

    

9.

Disassemble the product into two binomials:


    
10.

Factorise:

   
11.

Write the numbers X and Y as follows:


    
12.

Factorise:

   
13.

Write the numbers X and Y as follows:


    
14.

Express the following expression as a binomial square:

   
15.

Express the following expression as a square of a binomial expression:

   
16.

Factorise:

   
17.

Factorise:

   
18.

Factorise:

   

19.

Expand the product to two members:

   
20.

Disassemble the product of binomials:

   
21.

Factorise using the sum of cubes of a binomial identity:


    
22.

Factorise using the difference of cubes identity:


    
23.

Factorise using the difference of cubes of a binomial identity:


    
24.

Factorise using the sum of cubes identity:


    
25.

Factorise using the difference of cubes identity:


    
26.

Factorise using the sum of cubes identity:


    
27.

Factorise using the sum of cubes identity:


    
28.

Factorise using the difference of cubes identity:


    

29.

Factorise using the difference of cubes identity:


    
30.

Is the expression a multiple of the expression ?

    
31.

Factorise:

   
32.

Factorise:

   
33.

Factorise:

   
34.

Factorise:

   
35.

Factorise:

   
36.

Factorise:

   
37.

Factorise:

   
38.

Factorise:

   

39.

Factorise:

   
40.

Factorise:

   
41.

Factorise:

   
42.

For each natural number r, is the term an even number?

    
43.

Factorise:

   
44.

Factorise:

   
45.

Factorise:

   
46.

Factorise:

   
47.

Factorise:


    
48.

Factorise:

   

49.

Factorise:

   
50.

Factorise:

   
51.

Factorise:


    
52.

Factorise:

   
53.

Factorise:

   
54.

Factorise:

   
55.

Factorise:

   
56.

Factorise:

   
57.

Factorise:

   
58.

Factorise:

   

59.

Factorise:

   
60.

Factorise:

   
61.

Factorise:

   
62.

Factorise:

   
63.

Factorise:

   
64.

Factorise:

   
65.

Factorise:

   
66.

Factorise:

   
67.

Disassemble:

   
68.

Disassemble:

   

69.

Disassemble:

   
70.

Disassemble:

   
71.

Factorize:


    
72.

Disassemble:

   
73.

Disassemble:

   
74.
Factorize the expression:

    
75.

Disassemble:

   
76.

Disassemble:

   
77.

Factorise:

   
78.
Factorize the expression:

    

79.

Disassemble expressions in a set of real numbers or write that this is not possible.













    
80.

Factorize:


    
81.
Factorize the expression:

    
82.
Factorize the expression:

    
83.
Factorize the expression:

    
84.
Factorize the expression:

    
85.
Factorize the expression:



For , calculate the value of the given expression.