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Please study
Algebra Glossary before Algebra Substitution
if you have not already done so.

Value of an Algebraic Expression

The literal numbers or variables in an algebraic expression
can take any value allotted to them.

Thus, by putting allotted numerical values in place of literal values,
the value of an algebraic expression can be found.

The method of putting allotted numerical numbers
in place of literal numbers is called SUBSTITUTION.

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Example 1 of Algebra Substitution :

If a = 2, b = 5, find the value of (i) 2a + b (ii) a +3b (iii) 10a - 4b

solution to Example 1 of Algebra Substitution :

substituting a = 2 and b = 5, we get
(i) 2a + b = 2x2 + 5 = 4 + 5 = 9.
(ii) a + 3b = 2 + 3x5 = 2 + 15 = 17.
(iii) 10a - 4b = 10x2 - 4x5 = 20 - 20 = 0.

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Example 2 of Algebra Substitution :

If x = 3, find the value of 3x2 - 5x + 10

solution to Example 2 of Algebra Substitution:

substituting x = 3, we get
3x2 - 5x + 10 = 3x32 - 5x3 + 10 = 3x9 - 15 +10 = 27-15+10 = 22.

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Example 3 of Algebra Substitution :

Solved Example 3 of Algebra Substitution :

If x = 5, y = -3 and z = 2, find the value ofx 2 + y2 + z2 -2xy -2yz -2zx.

solution to Example 3 of Algebra Substitution :

substituting x = 5, y = -3 and z = 2, we get
x2 + y2 + z2 - 2xy - 2yz - 2zx
= (5)2+ (-3) 2 + (2) 2 - 2(5)(-3) - 2 (-3)(2) - 2(2)(5)

= 25 + 9 + 4 - (-30) - (-12) - (20) = 38 +30 +12 -20 = 60.

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