Question

How to factor polynomials with different degrees?

What if the degree of the polynomials are greater than 2 like:

1) a^3 + 8b^6

2) a^3 - 27b^9

3) x^6 + y^9

Answers

1) a3 + 8b?

= a3 + (2b2)3

= (a + 2b2).(a2 - a.2b2 + (2b2)2)............[ as x3 + y3 = (x + y).(x2 - xy + y2) ]

= (a + 2b2).(a2 - 2ab2 + 4b?)

2) a3 - 27b?

= a3 - (3b3)3

= (a - 3b3).(a2 + a.3b3 + (3b3)2)............[ as x3 - y3 = (x - y).(x2 + xy + y2) ]

= (a - 3b3).(a2 + 3ab3 + 9b?)

3) x? + y?

= (x2)3 + (y3)3

= (x2 + y3).((x2)2 - x2.y3 + (y3)2)............[ as x3 + y3 = (x + y).(x2 - xy + y2) ]

= (x2 + y3).(x? - x2.y3 + y?)

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