Year 10: Symbolic substitution in algebraic expressions

What is symbolic substitution?

Symbolic substitution is a technique used in algebra where you replace variables in an algebraic expression with specific values. This allows you to evaluate the expression for those particular values.

How to do it

1. Identify the variable: First, determine the variable(s) in the expression that you need to substitute.
2. Substitute the value: Replace the variable with the given value. For example, if $x=2$, you replace 'x' with '2'.
3. Simplify: After substituting, simplify the expression using the order of operations (BODMAS/PEMDAS).

Examples

Example 1: Evaluate $3x+2$ when $x=5$

Substitute x with 5: $3\left(5\right)+2$

Simplify: $15+2=17$

Example 2: Evaluate $2y^2-y$ when $y=-1$

Substitute y with -1: $2{(-1)}^2-(-1)$

Simplify: $2\left(1\right)+1=2+1=3$

Important notes

• Make sure to follow the order of operations (BODMAS/PEMDAS).
• Double-check your substitution to avoid errors.
• This technique is often used to solve equations and understand how variables relate to the expression's value.