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

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jerichorayel's profile pic

jerichorayel | College Teacher | (Level 2) Senior Educator

Posted on

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 =   1x^3  + 3x^2(2) + (2^2)(3x) + 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 

 

terrence958's profile pic

terrence958 | Student, Grade 9 | (Level 1) Honors

Posted on

(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

chaobas's profile pic

chaobas | College Teacher | (Level 1) Valedictorian

Posted on

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

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