what is the product of this(x+2)^3

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for this one you can solve this in many ways.

(x+2)^3 = (x+2)(x+2)(x+2) --> foil out the the first two factors

= (x^2 + 4x + 4) (x+2) then distribute the thir factor

= x^3 + 2x^2 + 4x^2 + 8x + 4x + 8 combine like terms

= x^3 + 6x^2 + 12x + 8

or you can do the pascals triangle

we go from the 1 3 3 1

(x+2)^3 = **1**x^3 + **3**x^2(2) + (2^2)(**3**x) + 2^3(**1**)

or

1(x)^3(-2)^0 + 3(x)^2(-2)^1 + 3(x)^2(-2)^2 + 1(x)^0(-2)^3 =

x^3 - 6x^2 + 12x - 8

combine like terms to have x^3 + 6x^2 + 12x + 8

hope this helps

Now (x+2)^3 is the form of (a+b)^3 : where a=x and b=3:

Now we have the general formula as

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

plugging we have the value

(x+2)^3 = x^3 + 2^3 + 3.x^2.2 + 3.x.2^2

=x^3+8+6x^2+12x

(x+2)^3=(x+2)(x+2)(x+2)

Now FOIL

(x+2)(x+2)(x+2)= x^3+6x^2+12x+8

or....

(x+2)(x+2)=x^2+4x+4

x^2+4x+4(x+2)=x^3+4x^2+4x+2x^2+8x+8+=x^3+6x^2+12x+8

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