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- GCE N(A)-Level A Maths
- Factorisation

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Try reviewing these fundamentals first

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Get Started Now- Intro Lesson9:45
- Lesson: 1a3:34
- Lesson: 1b3:00
- Lesson: 2a3:52
- Lesson: 2b2:16
- Lesson: 3a3:08
- Lesson: 3b4:02
- Lesson: 4a3:55
- Lesson: 4b2:44
- Lesson: 4c2:50

Basic Concepts: Factor by taking out the greatest common factor, Factor by grouping, Factoring difference of squares: $x^2 - y^2$

$\bullet$ Sum of cubes: $a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2})$

$\bullet$ Difference of cubes: $a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})$

$\bullet$ SOAP: $a^{3} \pm b^{3} = (a[same sign]b)(a^{2}[opposite sign]ab[always positive]b^{2})$

$\bullet$Things to consider before using the difference of cubes formula:

1. Is there a 'difference' sign? Are there two cubed terms?

2. Are the terms in order? (i.e. in descending order of degrees)

3. Is the first term positive?

4. Is there a Greatest Common Factor (GCF)?

- IntroductionIntroduction to Factoring difference of cubes
i. What is difference of cubes?

ii. How can difference of cubes be factored?

- 1.
**Factoring Using the Difference of Cubes Formula**Factor the following expressions:

a)$x^{3} - 8$b)$x^{3} - \frac{1}{27}$ - 2.
**Factoring Using the Difference of Cubes Formula - Extended**Factor the following expressions:

a)$27y^{3} - 1$b)$8x^{3} - 27$ - 3.
**Factoring Binomials with 2 variables**Factor the following expressions:

a)$27x^{3} - 64y^{3}$b)$x^{3}y^{6} - 125$ - 4.
**First Factor the Greatest Common Factor, Then Apply the Difference of Cubes Formula**Factor the following expressions:

a)$16x^{3} - 54$b)$-8x^{3} + 1$c)$81x^{4} - 3xy^{3}$

5.

Factorisation

5.1

Factorise by taking out the greatest common factor

5.2

Factorise by grouping

5.3

Factorising perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$

5.4

Factorising difference of squares: $x^2 - y^2$

5.5

Factorise trinomials

5.6

Solving polynomials with unknown coefficients

5.7

Solving polynomials with unknown constant terms

5.8

Factorising difference of cubes: $a^3-b^3$

5.9

Factorising sum of cubes: $a^3+b^3$