Year 7: Symbolic Substitution in Algebraic Expressions

What is Symbolic Substitution?

Symbolic substitution means replacing a variable in an expression with another expression (not just a number). This is useful when working with multiple variables or when one variable is defined in terms of another.

How to do Symbolic Substitution

1. Identify the variable to substitute: Find the letter you'll be replacing
2. Use brackets: Replace the variable with the expression in brackets: (expression)
3. Simplify: Expand and collect like terms

Examples

Example 1: In 2x + 3, substitute x with (a + 1)

1. Substitute: 2(a + 1) + 3
2. Expand: 2a + 2 + 3
3. Simplify: 2a + 5

Example 2: In x² - 2x, substitute x with (y + 2)

1. Substitute: (y + 2)² - 2(y + 2)
2. Expand (y + 2)²: y² + 4y + 4
3. Expand -2(y + 2): -2y - 4
4. Combine: y² + 4y + 4 - 2y - 4 = y² + 2y

Example 3: In 3x + y, substitute x with 2 and y with (z - 1)

1. Substitute: 3(2) + (z - 1)
2. Calculate and simplify: 6 + z - 1 = z + 5

Why Use Symbolic Substitution?

• To express one variable in terms of another
• To simplify complex algebraic expressions
• To understand relationships between variables