a^3 - b^3 = (a - b) (a^2 + ab + b^2)
I don't understand how we even came up with ab ie (a^2 + AB +b^2). How was the AB calculated? I try to understand the actually steps in Math and I do not understand how ab came into fruition
Difference in Perfect Cubes...please help?
2016-06-20 7:06 am
回答 (2)
2016-06-20 7:14 am
a³ - b³
= a³- a²b + a²b - ab² + ab² - b³ ...... - a²b + a²b - ab² + ab² = 0
= (a³- a²b) + (a²b - ab²) + (ab² - b³) ...... grouping
= a²(a - b) + ab(a - b) + b²(a - b) ...... take out the common factors
= (a - b)(a² + ab + b²) ...... take out the common factor (a - b)
= a³- a²b + a²b - ab² + ab² - b³ ...... - a²b + a²b - ab² + ab² = 0
= (a³- a²b) + (a²b - ab²) + (ab² - b³) ...... grouping
= a²(a - b) + ab(a - b) + b²(a - b) ...... take out the common factors
= (a - b)(a² + ab + b²) ...... take out the common factor (a - b)
2016-06-20 7:13 am
Well,
let's start from the RHS :
(a - b) (a^2 + ab + b^2) = a(a^2 + ab + b^2) - b(a^2 + ab + b^2)
= a^3 + a^2b + ab^2 - a^2b - ab^2 - b^3 <--- terms in the middle cancel
= a^3 - b^3
there is nothing to "understand" : just learn this identity by heat
hope it' ll help !!
let's start from the RHS :
(a - b) (a^2 + ab + b^2) = a(a^2 + ab + b^2) - b(a^2 + ab + b^2)
= a^3 + a^2b + ab^2 - a^2b - ab^2 - b^3 <--- terms in the middle cancel
= a^3 - b^3
there is nothing to "understand" : just learn this identity by heat
hope it' ll help !!
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