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

Simplifying algebraic expressions

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The greatest common divisor and the least common multiple
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Quadratic equation
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:simplifying_algebraic_expressions/3547/


Example 1.

Simplify the expression:


    
Example 2.

Simplify the following expressions:








    
3.

Determine the highest common factor and the least common multiple of the following expressions:






    
4.

Simplify the expression:


    
5.

Simplify:


    
6.

Simplify the expression and write the result as a product of linear factors: .

    
7.

Determine natural numbers to which the following properties apply:




    
8.

Simplify the expression:


    

9.

Simplify:


    
10.

Simplify the expression


    
11.

Determine the greatest common divisor and the least common multiple of the following three terms:






    
12.

Find the HCF and LCM of the following pairs:


  • ,

  • ,

  • ,

  • , ,

   
13.

Simplify the following:












    
14.

Simplify:


    
15.

Determine the highest common factor and the least common multiple of the following expressions:






    
16.

Simplify the expression:


    
17.

Simplify the expression:

   
18.

Determine the greatest common divisor and the least common multiple of the following three terms:






    

19.

Simplify the expression:


    
20.

Simplify the following examples.


  • Add the terms and .


  • Subtract the terms and .


  • Multiply the expressions and .

    
21.

Simplify the following:





    
22.

Group like terms and simplify:







    
23.

Simplify:

   
24.

Simplify:












    
25.

Simplify:

   
26.

Calculate the quotient.





    
27.

Simplify and factorise:

   
28.

Factorize using a common factor:


    

29.

In the expression highlights the common factor:


    
30.

Factorize the expression:


    
31.

Factorise:

   
32.

Factorize:


    
33.

Factorize:


    
34.

Factorize:


    
35.

Factorize:


    
36.

Factorize the expression:


    
37.

Factorize:


    
38.

Factorize:


    

39.

Factorize:


    
40.

Factorize:


    
41.

Factorize:


    
42.

Factorize:


    
43.

Simplify:


    
44.

Simplify:


    
45.

Simplify:


    
46.

Simplify:


    
47.

We simplify:


    
48.

Simplify:


    

49.

Simplify following algebraic expressions:











    
50.
Prove that:

.

    
51.

Simplify:


    
52.
Prove that:

    
53.
Prove that:

.

    
54.
Show that:

    
55.
Show that:

    
56.

Express as a square of a binomial expression:

   
57.
Show that:

    
58.

Express the following expression as a binomial square:

   

59.
Show that:

    
60.

Express the following expression as square of a binomial:

   
61.

Express the following expression as square of a binomial:

   
62.

Factorize:


    
63.

Express the following expression as square of a binomial expression:

   
64.

Factorise:

   
65.

Express the following expression as square of a binomial expression:

   
66.

Factorise:

   
67.

Express the following expression as square of a binomial:

   
68.

Factorise:

   

69.

Express the following expression as square of a binomial expression:

   
70.

Factorise:

   
71.

Express the following expression as square of a binomial expression:

   
72.

Factorise:

   
73.

Express the following expression as square of a binomial expression:

   
74.

Factorise:

   
75.

Factorise:

   
76.

Factorise:

   
77.

Factorise:

   
78.

Factorise:

   

79.

Using the formula of the squares of binomial expressions, calculate:

   
80.

Factorise:

   
81.

Factorise:

   
82.

Factorise:

   
83.

Factorise:

   
84.

Factorise:

   
85.

Factorise:

   
86.

Using the formulas of the difference of two squares, calculate:

   
87.

Factorise:

   
88.

Using the formulas for the difference of two squares, calculate:

   

89.

Factorise:

   
90.

Using the formula of the squares of binomial expressions, calculate:

   
91.

Factorise:

   
92.
Expand the expression:

    
93.
Expand the expression:

    
94.
Expand the expression:

    
95.
Factorize the expression:

    
96.
Expand the expression:

    
97.
Expand the expression:

    
98.
Expand the expression:

    

99.
Expand the expression:

    
100.
Expand the expression:

    
101.
Expand the expression:

    
102.
Expand the expression:

    
103.
Expand the expression:

    
104.
Expand the expression:

    
105.
Expand the expression:

    
106.
Factorize the expression:

    
107.
Factorize the expression:

    
108.
Expand the expression:

    

109.
Factorize the expression:

    
110.
Factorize the expression:

    
111.
Expand the expression:

    
112.
Expand the expression:

    
113.
Expand the expression:

    
114.
Expand the expression:

    
115.
Expand the expression:

    
116.
Factorize the expression:

    
117.
Expand the expression:

    
118.
Factorize and simplify the fraction:

    

119.
Factorize the expression:

    
120.
Factorize the expression:

    
121.
Factorize and simplify the fraction:

    
122.
Factorize and simplify the fraction:

    
123.
Factorize and simplify the fraction:

    
124.
Factorize and simplify the fraction:

    
125.
Factorize the expression:

    
126.
Factorize the expression:

    
127.

Expand the expression:


    
128.

Expand the following using binomial theorem: