Using the binomial theorem, expand (x + 3)^4 and identify the coefficient of x^2.

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Multiple Choice

Using the binomial theorem, expand (x + 3)^4 and identify the coefficient of x^2.

Explanation:
The binomial theorem lets us expand (x + 3) to the form of a sum of terms where the x-power decreases as we move through the terms: x^4, x^3, x^2, x, and the constant term, each with a coefficient C(4,k) and a 3^k factor. To get the coefficient of x^2, we need the term where the x-power is 2. That occurs when k = 2, giving the term C(4,2) x^2 3^2 = 6 x^2 * 9 = 54 x^2. So the coefficient of x^2 is 54.

The binomial theorem lets us expand (x + 3) to the form of a sum of terms where the x-power decreases as we move through the terms: x^4, x^3, x^2, x, and the constant term, each with a coefficient C(4,k) and a 3^k factor.

To get the coefficient of x^2, we need the term where the x-power is 2. That occurs when k = 2, giving the term C(4,2) x^2 3^2 = 6 x^2 * 9 = 54 x^2. So the coefficient of x^2 is 54.

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