Question

factorise a3-a2b2-ab+b3​

Answer 1

Answer:

The factors of a3 – a2b2 – ab + b3 are [a2 – b] and[a – b2]

Step-by-step explanation:

Regrouping the 1st 2 terms we have,

a3 – a2b2 = a2[a-b2] -------eq 1

Regrouping the last 2 terms we have,

– ab + b3 = -b[a-b2] -------eq 2

∵ we have to make common parts in both eq 1 and 2

Combining eq 1 and 2

a3 – a2b2 – ab + b3 = a2[a-b2] -b[a-b2]

= [a2 – b][a – b2]

Hence the factors of a3 – a2b2 – ab + b3 are [a2 – b] and[a – b2]

Answer 2

Answer:

The factors of a3 – a2b2 – ab + b3 are [a2 – b] and[a – b2]

Step-by-step explanation:

Regrouping the 1st 2 terms we have,

a3 – a2b2 = a2[a-b2] -------eq 1

Regrouping the last 2 terms we have,

– ab + b3 = -b[a-b2] -------eq 2

∵ we have to make common parts in both eq 1 and 2

Combining eq 1 and 2

a3 – a2b2 – ab + b3 = a2[a-b2] -b[a-b2]

= [a2 – b][a – b2]

Hence the factors of a3 – a2b2 – ab + b3 are [a2 – b] and[a – b2]

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