1. 2. Algebraic manipulation
Study guide
2. Algebraic manipulation

2. Adding and subtracting like terms
Algebraic terms are separated by a + and ‒ in an algebraic expression. The algebraic expression
3x + 5y ‒ 2z has three terms 3x, 5y and 2z.
To add and subtract algebraic terms
Find the like terms.
Only add or subtract like terms.
Add or subtract the coefficients of the like terms.
HSC Hint – Circle like terms including the sign in front of the term. Add or subtract the circled like terms.

3. Multiplication and division of algebraic terms
Algebraic terms are multiplied and divided to form a single algebraic expression.
To multiply and divide algebraic terms
Write in expanded form.
Multiply and divide the coefficients and pronumerals.
Write pronumerals in alphabetical order and express in index notation.
HSC Hint – Cancelling numbers in an algebraic fraction makes the calculations easier.

4. Expanding algebraic expressions
Multiply the term outside the grouping symbol by the:
First term inside the grouping symbol.
Second term inside the grouping symbol.
Simplify and collect like terms if required.
HSC Hint – Remember to multiply the second term by the term outside the grouping symbol.

5. Factorising algebraic expressions
Factorising is the reverse process to expanding.
Find the largest factor of each term or the HCF.
Write the HCF outside the grouping symbol.
Divide the HCF into each term to find the terms inside the grouping symbols.
Check the factorisation by expanding the expression.
HSC Hint – Expand the answer to check for accuracy.

6. Substitution
Substitution involves replacing the pronumeral in an algebraic expression with one or more numbers.
To substitute values:
Write the algebraic expression.
Replace the variables in the expression with the numbers given in the question.
Evaluate using the calculator.
Write the answer to the specified level of accuracy and correct units if necessary.
HSC Hint – Show the substitution step. Marks are often awarded for this step.

7. Linear equations
An linear equation is a mathematical statement that says that two things are equal such as
To solve a linear equation
Perform the opposite operation (+ and –, × and ÷).
Add/subtract the same number to both sides of the equation.
Multiply/divide both sides of the equation by the same number.
HSC Hint – Do one step at a time and set work out down the page. One equal sign per line.

8. Equations with fractions
Use the same steps as linear equations. It is often beneficial to multiply all terms by the lowest common denominator to remove the fractions.
Perform the opposite operation (+ and –, × and ÷).
Add/subtract the same number to both sides of the equation.
Multiply/divide both sides of the equation by the same number.
HSC Hint – Multiply all the denominators together to obtain a common denominator.

9. Using formulas
A formula is a mathematical relationship between two or more variables such as
Using a formula to solve a problem.
Write the formula.
Replace the variables in the formula with the numbers given in the question.
Evaluate using the calculator.
Write the answer to the specified level of accuracy and correct units if necessary.
HSC Hint – Check your solution by substituting the answer back into the formula.