The formula
For example, the expression x3 - 8y3 can be expanded as follows:
Working backwards - Expansion
Since the opposite working of this formula is one step and requires almost no simplification, it is better to see an example of how this formula is applied in a problem like
On comparing the numerator with the RHS of the above formula, it is a difference of two cubes, x3 and 43. So, factoring it, you get:
a3 - b3 = (a - b)(a2 + ab + b2)Working forwards - Factorization
For example, the expression x3 - 8y3 can be expanded as follows:
= (x)3 - (2y)3
= (x - 2y)(x2 + (x)(2y) + (2y)2)
= (x - 2y)(x2 + 2xy + 4y2).. which is the factored form of x3 - 8y3
Working backwards - Expansion
Since the opposite working of this formula is one step and requires almost no simplification, it is better to see an example of how this formula is applied in a problem like
x2 + 4x + 16 x + 4
In the above example, if we multiply the fraction by
| x - 4 |
| x - 4 |
x2 + 4x + 16 x + 4 ×
x - 4 x - 4
=
| (x2 + 4x + 16) (x - 4) |
| (x - 4) (x + 4) |
On comparing the numerator with the RHS of the above formula, it is a difference of two cubes, x3 and 43. So, factoring it, you get:
.. which is a simplified form of the original expression.
x3 - 43 (x + 4) (x - 4)
