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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]
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