Algebra Homework Help : Substitution in Algebraic Expressions

How to Simplify Algebraic Expressions by Substitution ?

Simplification and evaluation of an algebraic expression is possible by substituting the various letter variables with given expressions and specific values. It is important to write each substitution in parentheses, and then simplify the expression carrying out the operations in the correct order (Parentheses, Exponents, Multiplication, Division, Addition and Subtraction).

Example :
Given b = -3, c = a³ and d = a + 2, simplify c(a - 3b) + 7a³b + a³d
Now, c(a - 3b) + 7a³b + a³d
= (a³) (a - 3(-3)) + 7a³(-3) + a³(a + 2)
[on substituting b everywhere by (-3), c by (a³), and d by (a + 2)]
= a⁴ + 9a³ - 21a³ + a⁴ + 2a³
= 2a⁴ - 10a³
The simplified result may also be written as 2a³(a - 5).

Practice Exercise for Algebra Module on Substitution in Algebraic Expressions