Question
Using Pascal’s Triangle, what is the fourth term in the expansion of (a+3)^4
when the expanded polynomial is written in standard form?
when the expanded polynomial is written in standard form?
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GPT 3.5
To find the fourth term in the expansion of (a + 3)^4 when written in standard form, we can use Pascal's triangle to determine the coefficients of the terms in the expansion.
The coefficients in the expansion of (a + b)^n are given by the entries in the nth row of Pascal's triangle.
The fourth row of Pascal's triangle is 1 4 6 4 1.
In the expansion of (a + 3)^4, the coefficients of the terms will be in the order: 1, 4, 6, 4, 1.
Therefore, the fourth term in the expansion of (a + 3)^4 is 6a^2 * 3^2 = 6a^2 * 9 = 54a^2.
The coefficients in the expansion of (a + b)^n are given by the entries in the nth row of Pascal's triangle.
The fourth row of Pascal's triangle is 1 4 6 4 1.
In the expansion of (a + 3)^4, the coefficients of the terms will be in the order: 1, 4, 6, 4, 1.
Therefore, the fourth term in the expansion of (a + 3)^4 is 6a^2 * 3^2 = 6a^2 * 9 = 54a^2.
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