Fun Factorising Quadratics: Easy Steps, Worksheets & Answers

Libby

18/10/2025

Maths

Maths topic review - FACTORISING

1,148

•

18 Oct 2025

•

2 pages

Fun Factorising Quadratics: Easy Steps, Worksheets & Answers

Name: Knowunity
Brand: Knowunity

Libby

@libbysnotes

This document covers factorising quadratics, difference of two squares, and... Show more

-factorising
- FACTORISING QUADRATICS
Factorise
x² + 7 x + 1 2
(x + 4)(x + 37
1.
2.
X²
3 x - 10
(x - 5)(x + 2)
because 4 x 3=12
4 + 3 = 7
be

Factorising Using Difference of Two Squares and Harder Quadratics

This page covers two advanced topics in quadratic factorisation: the difference of two squares and factorising harder quadratic equations.

Difference of Two Squares

Definition: The difference of two squares is an algebraic expression where a squared term is subtracted from another squared term.

The page provides two examples of factoring difference of squares examples with answers:

x² - 36 Solution: $x + 6$ $x - 6$
4x² - 25 Solution: $2x + 5$ $2x - 5$

Highlight: The general form for the difference of two squares is a² - b², which factors to $a + b$ $a - b$ .

These examples are excellent for students studying difference of two squares Grade 8 level mathematics and preparing for difference of two squares exam questions.

Factorising Harder Quadratic Equations

The page then moves on to factorising harder quadratic equations, providing a comprehensive example:

x² - x - 15

Example: The solution process involves identifying factors of -15 that add up to -1, which are -5 and 4. The factored form is $x - 5$ $x + 3$ .

Another example demonstrates factorising a quadratic expression with a common factor:

2x² - 6x + 5x - 15

Example: This is solved by first factoring out the common factor, then grouping the remaining terms: 2x $x - 3$ + 5 $x - 3$ , which simplifies to $2x + 5$ $x - 3$ .

These examples align with Maths Genie Factorising Harder Quadratics content and are suitable for GCSE 1-9 Factorising Harder Quadratics preparation.

Vocabulary: Grouping: A method used in factoring where terms are arranged to identify common factors.

This page provides valuable practice for students working on factorising harder quadratic equations worksheets and preparing for advanced algebra exams.

Factorising Quadratics

This page focuses on the fundamental concept of factorising quadratics step by step. It provides clear examples to help students understand the process of breaking down quadratic expressions into their factors.

Definition: Factorising quadratics involves finding two binomials that, when multiplied together, produce the original quadratic expression.

The page presents two examples of factorising quadratics step by step:

x² + 7x + 12 Solution: $x + 4$ $x + 3$

Example: In this case, we need to find two numbers that multiply to give 12 and add up to 7. These numbers are 4 and 3.

x² + 3x - 10 Solution: $x - 2$ $x + 5$

Example: Here, we look for two numbers that multiply to give -10 and add up to 3. These numbers are -2 and 5.

Highlight: The key to factorising quadratics is identifying the pair of numbers that satisfy both the coefficient of x and the constant term in the quadratic expression.

This page serves as an excellent resource for students preparing for their GCSE 1-9 Factorising Quadratics exams, providing clear examples and solutions that align with Corbettmaths Factorising Quadratics approach.

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Maths

18 Oct 2025

1,148

2 pages

Fun Factorising Quadratics: Easy Steps, Worksheets & Answers

Libby @libbysnotes

This document covers factorising quadratics, difference of two squares, and harder quadratic equations, providing step-by-step examples and solutions for each type of problem.

• Factorising quadratics step by stepis... Show more

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Factorising Using Difference of Two Squares and Harder Quadratics

This page covers two advanced topics in quadratic factorisation the difference of two squares and factorising harder quadratic equations.

Difference of Two Squares

Definition The difference of two squares is an algebraic expression where a squared term is subtracted from another squared term.

The page provides two examples of factoring difference of squares examples with answers

x² - 36 Solution $x + 6$ $x - 6$
4x² - 25 Solution $2x + 5$ $2x - 5$

Highlight The general form for the difference of two squares is a² - b², which factors to $a + b$ $a - b$ .

These examples are excellent for students studying difference of two squares Grade 8 level mathematics and preparing for difference of two squares exam questions.

Factorising Harder Quadratic Equations

The page then moves on to factorising harder quadratic equations, providing a comprehensive example

x² - x - 15

Example The solution process involves identifying factors of -15 that add up to -1, which are -5 and 4. The factored form is $x - 5$ $x + 3$ .

Another example demonstrates factorising a quadratic expression with a common factor

2x² - 6x + 5x - 15

Example This is solved by first factoring out the common factor, then grouping the remaining terms 2x $x - 3$ + 5 $x - 3$ , which simplifies to $2x + 5$ $x - 3$ .

These examples align with Maths Genie Factorising Harder Quadratics content and are suitable for GCSE 1-9 Factorising Harder Quadratics preparation.

Vocabulary Grouping A method used in factoring where terms are arranged to identify common factors.

This page provides valuable practice for students working on factorising harder quadratic equations worksheets and preparing for advanced algebra exams.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Factorising Quadratics

Definition Factorising quadratics involves finding two binomials that, when multiplied together, produce the original quadratic expression.

The page presents two examples of factorising quadratics step by step

x² + 7x + 12 Solution $x + 4$ $x + 3$

Example In this case, we need to find two numbers that multiply to give 12 and add up to 7. These numbers are 4 and 3.

x² + 3x - 10 Solution $x - 2$ $x + 5$

Example Here, we look for two numbers that multiply to give -10 and add up to 3. These numbers are -2 and 5.

Highlight The key to factorising quadratics is identifying the pair of numbers that satisfy both the coefficient of x and the constant term in the quadratic expression.

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What is the Knowunity AI companion?

Where can I download the Knowunity app?

You can download the app from Google Play Store and Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

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4.9/5

App Store

4.8/5

Google Play

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user