Summary
When developing algebraic expressions it is often useful to factorise the expression to familiar components. Through factorisation, one can increases both the readability and manipulability of the expression. This article summarises the common algebra factorisation relationships.
Common Algebra Factorisation Relationship
| Ref | Formula |
|---|---|
| 1 | $ x^2 - y^2 = (x-y)(x+y) $ |
| 2 | $ x^3 - y^3 = (x-y)(x^2 + xy + y^2) $ |
| 3 | $ x^3 + y^3 = (x+y)(x^2 - xy +y^2) $ |
| 4 | $ x^4 - y^4 = (x-y)(x+y)(x^2 + y^2) $ |
| 5 | $ x^5 + y^5 = (x + y)(x^4 - x^3y + x^2y^2 - xy^3 + y^4) $ |
| 6 | $ x^n - y^n = (x - y)(x^{n-1} + x^{n-2}y + x^{n-3}y^2 + ... + y^{n-1}) $ |
| 7 | $ x^2 + 2xy + y^2 = (x+y)^2 $ |
| 8 | $ x^2 + ax +b = (x + c)(x + d) $ where $ c = a - d $ and $ d = \frac{1}{2} \left( \pm \sqrt{a^2 + 4b} - a \right) $ |
| 9 | $ x^2 + y^2 + z^2 + 2yz + 2xz + 2xy = (x + y + z)^2 $ |
| 10 | $ x^2 + y^2 + z^2 - 2yz = (x - y - z)(x + y + z) $ |
| 11 | $ x^2 + y^2 + z^2 - 2xy -2xz + 2yz = (x - y - z)^2 $ |
Further Reading
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