Question

factorise
a3 - a²b + ab2 - b3​

Answer 1

Answer:

(a - b) • (a2 + ab + b2) .

Step-by-step explanation:

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

Answer:

$\large ( {a}^{2} + {b}^{2} )(a - b)$

Step-by-step explanation:

${a}^{3} - {a}^{2} b + a {b}^{2} - {b}^{3}$

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

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