Find the expansion of (r + 4)^3.

r^3 + (3r^2)(4) + 3r16 + 64?

yes. To get full credit though, you probably need to combine factors:

r^3 + 12r^2 + 48r + 64

Thank you!

To find the expansion of (r + 4)^3, we can use the binomial theorem. According to the binomial theorem, the expansion of (a + b)^n can be found using the formula:

(a + b)^n = C(n, 0) * a^(n - 0) * b^0 + C(n, 1) * a^(n - 1) * b^1 + C(n, 2) * a^(n - 2) * b^2 + ... + C(n, n) * a^(n - n) * b^n

In the expansion of (r + 4)^3, a = r, b = 4, and n = 3.

Let's substitute the values into the formula:

(r + 4)^3 = C(3, 0) * r^(3 - 0) * 4^0 + C(3, 1) * r^(3 - 1) * 4^1 + C(3, 2) * r^(3 - 2) * 4^2 + C(3, 3) * r^(3 - 3) * 4^3

Simplifying the equation:

= C(3, 0) * r^3 * 4^0 + C(3, 1) * r^2 * 4^1 + C(3, 2) * r^1 * 4^2 + C(3, 3) * r^0 * 4^3

Now let's calculate the binomial coefficients:

C(3, 0) = 1
C(3, 1) = 3
C(3, 2) = 3
C(3, 3) = 1

Substituting the values back into the equation:

= 1 * r^3 * 4^0 + 3 * r^2 * 4^1 + 3 * r^1 * 4^2 + 1 * r^0 * 4^3

Finally, simplify the equation to get the expansion:

= r^3 + 3r^2 * 4 + 3r * 16 + 1 * 64

= r^3 + 12r^2 + 48r + 64

So, the expansion of (r + 4)^3 is r^3 + 12r^2 + 48r + 64.