Question

Factors of (a + b)3 - (a - b)3 is :

(A) 2ab(3a2 + b2) (B) ab(3a2 + b2) (C) 2b(3a2 + b2) (D) 3a2 + b2​

Answer 1

Answer:

a3 + b3

Step-by-step explanation:

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

So let us expand it(a+b)^3

So let us expand it(a+b)^3= (a+b) (a+b) (a+b)

So let us expand it(a+b)^3= (a+b) (a+b) (a+b)={(a+b) (a+b)} (a+b)

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)

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)

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)

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)

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

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

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

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

Let us graphically represent this formula:

Let us assume

Let us assumea = 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 friend ;)

Answer 2

Answer:

a3+b3

Step-by-step explanation: