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19 Dec 2025

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3 pages

Mastering Factorisation: Learn with a Clear Step-by-Step Example

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Factorising is a key algebraic skill that helps you simplify... Show more

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Factorising means put into
brachets
Step 1: decide how many
brackets you need to put the equation in
* Something in common = 1 brachet
*

Factorising Basics

Factorising means putting expressions into brackets to simplify them. The first step is deciding how many brackets you need - one bracket if terms share a common factor, or two brackets if they don't.

Look for common factors between terms. For example, in 10x² + 15xy, both terms share a factor of 5, so we need just one bracket. We place the common factor (5) outside the bracket like this: 5( ).

Next, determine what goes inside the bracket by dividing each term by the common factor. For 10x²÷5 = 2x and 15xy÷5 = 3y, our answer becomes 5 $2x + 3y$ . Always check your answer by expanding the brackets to ensure you get the original expression.

Remember: Factorising is like reverse-expanding brackets. If you can spot what's common between terms, you're halfway there!

Factorising Quadratics

When factorising expressions like x² + 9x + 20 that have no common factor across all terms, we need two brackets. These quadratic expressions typically follow the pattern ax² + bx + c.

Start by finding the factor pairs of the last number (c). For 20, the factor pairs are 1×20, 2×10, and 4×5. We need to find which pair adds up to the middle coefficient (9). Since 4+5=9, we'll use these numbers.

Write out your brackets as (x )(x ) because multiplying these gives us x². Then insert the factors: $x+4$ $x+5$ . To check, multiply these brackets - you should get x² + 9x + 20.

Pro tip: When factorising quadratics, always look for the factor pair that both multiplies to give the last term AND adds to give the middle coefficient.

Completing the Factorisation

After identifying your factors, place them in brackets with the x-terms. For example, with x² + 9x + 20, our final answer is $x+4$ $x+5$ . You can verify this works because 4×5=20 and 4x+5x=9x.

When factorising expressions with common factors first, like 9x² + 6x, identify what's common to all terms (in this case 3x) and factor it out: 3x $3x + 2$ . Always check your work by expanding to confirm you get the original expression.

Practice makes perfect with factorising. Try working through examples of increasing difficulty to build your confidence. You'll soon find yourself spotting patterns quickly!

Quick check: After factorising, always expand your brackets to make sure you get back to the original expression. If not, you've made a mistake somewhere.

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19 Dec 2025

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3 pages

Mastering Factorisation: Learn with a Clear Step-by-Step Example

StudyWfb

@fb_emmf

Factorising is a key algebraic skill that helps you simplify expressions by putting terms into brackets. This method makes complex expressions easier to understand and solve. We'll look at different factorising techniques for various types of expressions.

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Factorising Basics

Remember: Factorising is like reverse-expanding brackets. If you can spot what's common between terms, you're halfway there!

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Factorising Quadratics

When factorising expressions like x² + 9x + 20 that have no common factor across all terms, we need two brackets. These quadratic expressions typically follow the pattern ax² + bx + c.

Write out your brackets as (x )(x ) because multiplying these gives us x². Then insert the factors: $x+4$ $x+5$ . To check, multiply these brackets - you should get x² + 9x + 20.

Pro tip: When factorising quadratics, always look for the factor pair that both multiplies to give the last term AND adds to give the middle coefficient.

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Completing the Factorisation

After identifying your factors, place them in brackets with the x-terms. For example, with x² + 9x + 20, our final answer is $x+4$ $x+5$ . You can verify this works because 4×5=20 and 4x+5x=9x.

Practice makes perfect with factorising. Try working through examples of increasing difficulty to build your confidence. You'll soon find yourself spotting patterns quickly!

Quick check: After factorising, always expand your brackets to make sure you get back to the original expression. If not, you've made a mistake somewhere.