Question

a^3 - a^2b + ab^ 2 - b^3​

Answer 1

Step-by-step explanation:

a3 + b3

First of all let us know what is (a+b)^3 (“^” This is a power symbol)

Since the expression is derived from (a+b)^3

So let us expand it

(a+b)^3

= (a+b) (a+b) (a+b)

={(a+b) (a+b)} (a+b)

={a(a+b) + b(a+b)} (a+b)

=(a^2 + ab + ab + b^2) (a+b)

=(a^2 + b^2 + 2ab) (a+b)

=a^2(a+b) + b^2(a+b) + 2ab(a+b)

=a^3 + a^2b + ab^2 + b^3 + 2a^2b + 2ab^2

=a^3 + b^3 + 3a^2b + 3ab^2

=a^3 + b^3 + 3ab(a+b)

Now when we have expanded (a+b)^3 = a^3 + b^3 + 3ab(a+b)

We can equate it

(a+b)^3 = a^3 + b^3 + 3ab(a+b)

(a+b)^3 - 3ab(a+b) = a^3 + b^3

a^3 + b^3 = (a+b)^3 - 3ab(a+b)

Let us graphically represent this formula:

Let us assume

a = 1cm and b = 2cm

(a+b)^3

which is equal to a^3 + b^3 + 3a^2b + 3ab^2

So when we make a cube by adding a+ b we get 3 times of a^2b and 3 times of ab^2

Hope this could help you

Thank you

Answer 2

Answer:

1. (a-b) ^3 = (a-b) (a-b) ^2

=(a-b) (a^2+b^2-2ab)

=a^3-b^3-3a^2b-3ab^2

=a^3-b^3-3ab(a-b)