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Study guide
2. Algebraic manipulation
Cambridge University Press
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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
1. Find the like terms.
2. Only add or subtract like terms.
3. 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.
Cambridge University Press
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Multiplication and division of
algebraic terms


Algebraic terms are multiplied and divided to form a
single algebraic expression.
To multiply and divide algebraic terms
1. Write in expanded form.
2. Multiply and divide the coefficients and
pronumerals.
3. Write pronumerals in alphabetical order and
express in index notation.
HSC Hint – Cancelling numbers in an algebraic fraction
makes the calculations easier.
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Expanding algebraic expressions
1.
Multiply the term outside the grouping symbol by the:
a. First term inside the grouping symbol.
b. Second term inside the grouping symbol.
a (b  c)  a  b  a  c
 ab  ac
2.
Simplify and collect like terms if required.
HSC Hint – Remember to multiply the second term by the
term outside the grouping symbol.
Cambridge University Press
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Factorising algebraic expressions
Factorising is the reverse process to expanding.
1. Find the largest factor of each term or the HCF.
2. Write the HCF outside the grouping symbol.
3. Divide the HCF into each term to find the terms inside
the grouping symbols.
4. Check the factorisation by expanding the expression.
HSC Hint – Expand the answer to check for accuracy.
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Substitution

Substitution involves replacing the pronumeral in an
algebraic expression with one or more numbers.
 To substitute values:
1. Write the algebraic expression.
2. Replace the variables in the expression with the
numbers given in the question.
3. Evaluate using the calculator.
4. 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.
Cambridge University Press
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Linear equations

An linear equation is a mathematical statement that says
that two things are equal such as x  4  7 .

To solve a linear equation
1. Perform the opposite operation (+ and –, × and ÷).
2. Add/subtract the same number to both sides of the
equation.
3. 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.
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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.
1. Perform the opposite operation (+ and –, × and ÷).
2. Add/subtract the same number to both sides of the
equation.
3. Multiply/divide both sides of the equation by the
same number.
HSC Hint – Multiply all the denominators together to obtain
a common denominator.
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Using formulas

A formula is a mathematical relationship between two or
more variables such as
.
D
ST
 Using a formula to solve a problem.
1. Write the formula.
2. Replace the variables in the formula with the
numbers given in the question.
3. Evaluate using the calculator.
4. 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.
Cambridge University Press
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