Question

Factorie (a+b) ³−(a−b) ³ .
a. 2ab(a+b)
b. 3ab(a+b)
c. 4ab(a+b)
d. a³ +b³

Answer 1

To factor the expression (a+b)³ - (a-b)³, use the difference of cubes formula:

Step-by-step explanation:

To factor the expression (a+b)³ - (a-b)³, we can use the formula for the difference of cubes: a³ - b³ = (a - b)(a² + ab + b²).

1. First, apply the formula to factor (a+b)³ as (a+b)(a² + ab + b²).
2. Next, apply the formula to factor (a-b)³ as (a-b)(a² - ab + b²).
3. Now, we can substitute these factors into the original expression [(a+b)(a² + ab + b²)] - [(a-b)(a² - ab + b²)].
4. Finally, simplify the expression to get the fully factored form.

Using the difference of cubes formula, the expression is simplified to (a + b - a + b)(a² + ab + b² + a² - ab + b²), which further simplifies to 2b(a² + b²).