Simplify the following expression. (x + 8)^3

Question

Simplify the following expression. (x + 8)^3

 

I have the answer as x^3+24. Is this correct?

Answer 1

(x + 8)³ = (x + 8)(x + 8)(x + 8)

 

                 = (x + 8)(x² + 16x + 64)

 

                 = x(x² + 16x + 64) + 8(x² + 16x + 64)

 

                 = x³ + 16x² + 64x + 8x² + 128x + 512

 

                  = x³ + 24x²  + 192x + 512 

Answer 2

Ah, if only it were that simple. Any expression if (a+b)^n has to be completely expanded to simplify.

In your case:

(x+8)^3=(x+8)(x+8)(x+8).

FOIL the first two terms to get 

(x^2+8x+8x+64)(x+8)

Simplify by collecting terms

(X^2+16x+64)(x+8)

FOIL again

X^3+16x^2+64x+8x^2+128x+512

Collect like terms again

x^3+24x^2+192x+512

And you're done!

 

Practice FOILing and combining like terms, and you'll have it down pat!

-W