expand- (x+3)^4

Answer 1

To expand (x+3)^4, we can use the binomial theorem. The binomial theorem states that for any real numbers a and b, and any positive integer n, the expansion of (a+b)^n can be represented by the sum of the binomial coefficients multiplied by the respective powers of a and b.

In this case, we have a = x and b = 3, and we want to find the expansion of (x+3)^4.

Using the binomial theorem, the expansion can be written as:

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

Simplifying further, we have:

1 * x^4 * 1 + 4 * x^3 * 3 + 6 * x^2 * 9 + 4 * x * 27 + 1 * 3^4

This simplifies to:

x^4 + 12x^3 + 54x^2 + 108x + 81

Therefore, the expanded form of (x+3)^4 is x^4 + 12x^3 + 54x^2 + 108x + 81.