Use the binomial Theroum to expand the expression and express the results in simplified form
(3X + 2)^3
http://en.wikipedia.org/wiki/Binomial_theorem
We will be happy to critique your thinking.
Thanks I come up with
27x^3 + 54x^2 + 36x + 8
Yes
thanks
To expand the expression (3X + 2)^3 using the binomial theorem, you can use the formula:
(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n
In this case, a represents 3X and b represents 2. The exponent n is 3.
Let's calculate the terms step-by-step:
Term 1:
C(3, 0) * (3X)^3 * 2^0
= 1 * 3^3 * X^3 * 1
= 27X^3
Term 2:
C(3, 1) * (3X)^2 * 2^1
= 3 * 3^2 * X^2 * 2
= 27X^2 * 2
= 54X^2
Term 3:
C(3, 2) * (3X)^1 * 2^2
= 3 * 3^1 * X^1 * 2^2
= 9X * 4
= 36X
Term 4:
C(3, 3) * (3X)^0 * 2^3
= 1 * 3^0 * X^0 * 2^3
= 1 * 8
= 8
Now let's add up all the terms:
(3X + 2)^3 = 27X^3 + 54X^2 + 36X + 8
Therefore, the expanded form of (3X + 2)^3 is 27X^3 + 54X^2 + 36X + 8.