MHB Is this the simplified form of (a + b)^3 - 8c^3?

[mathdad]

Factor (a + b)^3 - 8c^3.

Is this the difference of cubes?

Formula:

x^3 - a^3 = (x - a)(x^2 + ax + a^2)

Let x = (a + b)

Let a = 8

(a + b - 8)((a + b)^2 + 8(a + b) + 64)

Correct?

 

[MarkFL]

I would begin by writing the expression as the difference of cubes:

$$(a+b)^3-8c^3=(a+b)^3-(2c)^3$$

Now apply the difference of cubes formula...:D

 

[mathdad]

Why did you write -8c^3 as -(2c)^3?

The number 8 is not part of c^3.

Are you saying that -8•c^3 = (-8c)^3?

 

[MarkFL]

Why did you write -8c^3 as -(2c)^3?

The number 8 is not part of c^3.

Are you saying that -8•c^3 = (-8c)^3?

I applied the exponential property:

$$x^ny^n=(xy)^n$$

Since $8=2^3$, we can write:

$$8c^3=2^3c^3=(2c)^3$$

 

[mathdad]

I got it now.