Question

a + b whole cube minus a minus b whole cube

Answer 1

(a+b)^3 - (a-b)^3 …. Expand cubic function.

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

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

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

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

Answer 2

(a + b)³ - (a - b)³ = 2b(3a² + b²)

Correct question : Simplify the expression (a + b)³ - (a - b)³

Given :

The expression (a + b)³ - (a - b)³

To find :

Simplify the given expression

Identity Used :

• (a + b)³ = a³ + 3a²b + 3ab² + b³

• (a - b)³ = a³ - 3a²b + 3ab² - b³

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

(a + b)³ - (a - b)³

Step 2 of 2 :

Simplify the given expression

We know that ,

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

Thus we get

(a + b)³ - (a - b)³

= (a³ + 3a²b + 3ab² + b³) - (a³ - 3a²b + 3ab² - b³)

= a³ + 3a²b + 3ab² + b³ - a³ + 3a²b - 3ab² + b³

= 6a²b + 2b³

= 2b(3a² + b²)

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