(x+4)^3 find product?

(x + 4)^3 is
(x + 4)(x + 4)(x + 4) =
(x + 4)(x^2 + 4x + 4x + 16) =
(x + 4)(x^2 + 8x + 16) =
x^3 + 8x^2 + 16x + 4x^2 + 32x + 64 =
x^3 + 12x^2 + 48x + 64 -- answer.

[ x + 4 ] [ x² + 8x + 16 ]
x³ + 8x² + 16x + 4x² + 32x + 64
x³ + 12x² + 48x + 64

(x + 4)^3
= x^3 + 12x^2 + 48x + 64

(x+4)^3 =
(x + 4)(x + 4)(x + 4) =
Apply FOIL to the first two bracketed terms .
Hence
(x^2 + 8x + 16)(x + 4)
We then apply an extension to FOIL by multiplying 'x' in the second bracket to each term in the first brackets. Then do the same with '4'.
Then collect 'like' terms.
Hence
x^3 + 8x^2 + 16x + 4x^2 + 32x + 64
x^3 + 12x^2 + 48x + 64 Done !!!

This can be done by using the Binomial Theroem
( x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3
Hence
(x + 4)^3 = x^3 + 3x^2(4) + 3x(4)^2 + 4^3 = x^3 + 12x^2 + 48x + 64 As above. !!!!

Hope that helps!!!!

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= (x + 4)(x^2 + 8x + 16)
= x^3 + 8x^2 + 16x + 4x^2 + 32x + 64
= x^3 + 12x^2 + 48x + 64