Question

2a(a-b) and 6ab(a+1)

Answer 1

Answer:

The answer to u r question is 8b^3

Step-by-step explanation:

(a+b)^3 = a^3 + 3a^2*b + 3ab^2 + b^3

(a-b)^3 = a^3 - 3a^2*b + 3ab^2 - b^3

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

now,

in this problem we will break it in parts first to make it easy ,

(2a+b)^3 ----------(a) [let this be part a

(2a-b)^3 ----------(b) [let this be part b

6b(2a+b)(2a-b)------------(c) [let this be part c

so we will start with a,

(2a+b)^3   [here 2a is 'a' and b is 'b' , so we will apply (a+b)^3]

=(2a)^3 + 3*(2a)^2*b + 3*2a*b^2 + b^3

=8a^3 + 12a^2*b + 6ab^2 + b^3  [lets just leave it like this ]

now we will solve b,

=(2a-b)^3   [here 2a is 'a' and b is 'b' , so we will apply (a-b)^3]

=(2a)^3 - 3*(2a)^2*b + 3*2a*b^2 - b^3

=8a^3 - 12a^2*b + 6ab^2 - b^3  [lets just leave it like this ]

now we will solve c,

6b(2a+b)(2a-b)   [here we will apply (a-b)(a+b)=a^2-b^2 as 2a as 'a' & b as 'b']

=6b((2a)^2 - b^2)

=6b(4a^2 - b^2)

=24a^2 *b -6b^3

now we will join a, b , c

that is a-b-c

=8a^3 + 12a^2*b + 6ab^2 + b^3 - [8a^3 - 12a^2*b + 6ab^2 - b^3 ]-[24a^2 *b -6b^3]

=8a^3 + 12a^2*b + 6ab^2 + b^3 - 8a^3 + 12a^2*b - 6ab^2 + b^3 - 24a^2 *b + 6b^3

=we will group the like terms ,

12a^2*b + 12a^2*b + b^3 + b^3- 24a^2 *b + 6b^3

=24a^2*b+2 b^3- 24a^2 *b + 6b^3

=2b^3+6b^3

=8b^3