Explain how you can prove the difference of two cubes identity. a^3 – b^3 = (a – b)(a^2 + ab + b^2)
2 answers:
Is this a mutiple choice or is this a give an example type deal
I already calculated this Let a^3 - b^3 = ? Add on both th side -3a^2b + 3ab^2 a^3 -3a^2b + 3ab^2 -b^3 = ? -3a^2b+3ab^2 The firs equation is = (a - b)^3 Then, (a - b)^3 = ? + 3a^2b - 3ab^2 Passing -3a^2b + 3ab^2 to the left side: But changing the sinal ? = (a - b)^3 + 3a^2b - 3ab^2 ? = (a - b)^3 + 3ab ( a - b) Putting (a - b) as commun factor ? = (a - b).[ 3ab + (a - b)^2 ] As (a - b)^2 = a^2 - 2ab + b^2 Then, ? = (a - b).[ 3ab + a^2 -2ab +b^2] ? = (a - b).( a^2 + ab + b^2) I hope this has helped
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Step-by-step explanation: hope this helps!!