College Algebra 110

[ddrake]

Please factor this equation for me showing ALL work step-by-step...

(X^3+27)

My book has (X+3)(X^2-3X+9) but this makes no sense to me.

Thank you

 

[merlin2007]

Please factor this equation for me showing ALL work step-by-step...

(X^3+27)

My book has (X+3)(X^2-3X+9) but this makes no sense to me.

Thank you

This is a sum of cubes - you should have been taught the formula (a^3 + b^3) = (a+b)(a^2 - ab + b^2)

The derivation is as follows

a^3 + (a^2)(b) - (a^2)(b) - (a)(b^2) + (a)(b^2) +b^3
= (a^2)(a+b) - (ab)(a+b) + (b^2)(a+b) = (a+b)(a^2 - ab + b^2)

I hope this helps, and if you need to, you can model the method in you specific case.

 

[tkhunny]

but this makes no sense to me.

Why do you quit when it makes no sense? Figure it out.

Multiply the two factors and watch it work. It will make sense. Can you multiply the factors?