Factoring formulas
Factorization, also known as Factoring, is a process of breaking down a large number into several small numbers. When these small numbers are multiplied, we will get the actual or original number.
1. a2 – b2 = (a + b)(a – b)
Example:
Factor: x2 – 4 y2
Solution:
x2 – 4 y2 = x2 – (2 y)2
x2 – 4 y2 = (x – 2 y)(x + 2 y)
2. a3 – b3 = (a – b)(a2 + ab + b2)
Example:
Factor: 8x3 – 27 y3
Solution:
8x3 – 27y3 = (2x)3 – (3 y)3
= (2x – 3y)[(2x)2 + (2x)(3 y) + (3 y)2 ]
= (2x – 3 y)(4x2 + 6xy + 9y2 )
3. a3 + b3 = (a + b)(a2 – ab + b2)
Example:
Factor: 54x3 + 16 y3
Solution:
54x3 + 16 y3 = 2(27x3 + 8 y3 )
= 2[(3x)3 + (2 y)3 ]
= 2(3x + 2 y)[(3x)2 – (3x)(2 y) + (2 y)2 ]
= 2(3x + 2 y)(9x2 – 6xy + 4 y2)
4. a4 – b4 = (a – b)(a + b)(a2 + b2)
Example:
Factor: 48x4 – 3y4
Solution:
48x4 – 3y4 = 3(16x4 – y4 )
= 3[(4x2)2 – ( y2)2]
= 3(4x2 – y2)(4x2 + y2 )
= 3(2x – y)(2x + y)(4x2 + y 2 )