Question

factorise it..............

Answer 1

a3-b3
Final result :
(a - b) • (a2 + ab + b2)
Reformatting the input :
Changes made to your input should not affect the solution:

(1): "b3" was replaced by "b^3". 1 more similar replacement(s).
Step by step solution :
Step 1 :
Trying to factor as a Difference of Cubes:
1.1 Factoring: a3-b3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3

Check : a3 is the cube of a1

Check : b3 is the cube of b1

Factorization is :
(a - b) • (a2 + ab + b2) .
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Answer 2

$a - b - {a}^{3} + b^{3}$

$= 1(a - b) - (a^{3} - {b}^{3} )$

$= 1(a - b) - (a - b)({a}^{2} + ab + b^{2} )$

$= (a - b)(1 - {a}^{2} - ab - {b}^{2} )$

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