Question

Explain how you can prove the difference of two cubes identity. a^3 – b^3 = (a – b)(a^2 + ab + b^2)

Answer 1

Answer:

Use the distributive property to multiply the factors on the right side of the equation.

Simplify the product by combining like terms.

Show that the right side of the equation can be written exactly the same as the left side.

Show that the right side of the equation simplifies to a cubed minus b cubed.

Step-by-step explanation:

thats the exact answer on egdenuity

Answer 2

Hello, It is very simples.

Look it :

Let a^3 - b^3 = ?

Add on both th side -3a^2b + 3ab^2

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

-3a^2b+3ab^2

The firs equation is = (a - b)^3

Then,

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

Passing -3a^2b + 3ab^2 to the left side:
But changing the sinal

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

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

Putting (a - b) as commun factor

? = (a - b).[ 3ab + (a - b)^2 ]

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

Then,

? = (a - b).[ 3ab + a^2 -2ab +b^2]

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

I hope helps!