%5E3-in-expanded-form.jpeg "(3x)^3 In Expanded Form")
(3x)^3 in Expanded Form
(3x)^3 is a cube of the binomial 3x. To find its expanded form, we need to follow the procedure of cube of a binomial.
Formula:
(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
In this case, a = 3x and b = x. Substituting these values into the formula, we get:
(3x)^3 = (3x)^3 + 3(3x)^2x + 3(3x)x^2 + x^3
Expanding the Formula:
Now, let's expand each term of the formula:
(3x)^3 = 27x^3
3(3x)^2x = 3(9x^2)x = 27x^3
3(3x)x^2 = 3(3x)x^2 = 27x^3
x^3 = x^3
Combining Like Terms:
Now, let's combine like terms:
(3x)^3 = 27x^3 + 27x^3 + 27x^3 + x^3
(3x)^3 = 81x^3 + x^3
(3x)^3 = 82x^3
Therefore, the expanded form of (3x)^3 is 82x^3.
