SOLUTION: Factor: How do I do this ? Factor: y^3+125 Thanks for your help and time, it's greatly appreciated !

Question 27740: Factor:
How do I do this ?
Factor:
y^3+125
Thanks for your help and time, it's greatly appreciated !
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Factor:
How do I do this ?
Factor:
y^3+125
y^3+125
=(y)^3 + (5)^3
=(y+5)[(y)^2 - (y)(5) + (5)^2]
(using formula:=(a)^3 + (b)^3 =(a+b)[(a)^2 - (a)X(b) + (b)^2]
In this problem a = y and b= 5)
=(y+5)(y^2-5y+25)
Note: The formula [(a)^3 + (b)^3] =(a+b)[(a)^2 - (a)(b) + (b)^2] is derived from the formula (a+b)^3 = a^3 +b^3 +3ab(a+b)
Now therefore we have a^3 +b^3 +3ab(a+b)= (a+b)^3
which implies
[a^3 +b^3] = (a+b)^3 - 3ab(a+b) (changing side then changing sign)
= p^3 - 3abp where p = (a+b)
= p[(p)^2 - 3ab]
=(a+b)[(a^2+b^2+2ab)-3ab]
=(a+b)[a^2+b^2+(2ab-3ab)] (by additive associativity)
=(a+b)[a^2+b^2+ -ab]
= (a+b)[(a)^2 - ab + (b)^2]

RELATED QUESTIONS
Factor: How do I do this ? Solve: 6x^2=12x Thanks for your help and time, it's... (answered by sdmmadam@yahoo.com)

Factor: How do I do this ? Factor 2x^3y^2-32xy^2 Thanks for your help and time,... (answered by Earlsdon)

Factor: How do I do this ? Solve: (z-5)(z+4)=52 Thanks for your help and time,... (answered by sdmmadam@yahoo.com)

Factor: 10a^3+3a-4 How do I do this ? Thanks for your help and time... (answered by Earlsdon)

How do I factor this polynomial .... c to the 3rd power + 125 Thanks for your... (answered by longjonsilver)

Factor: 9x^2-12x-5 How do I do this ? Thanks for your help and time... (answered by sdmmadam@yahoo.com)

Factor: 3x^2+x+1 How do I do this ? Thanks for your help and time... (answered by stanbon)

Factor: a^2-6a-27 How do I do this ? Thanks for your help and time... (answered by sdmmadam@yahoo.com)

How do I factor 2x^2+4x+3=0? Your help is greatly... (answered by scott8148)