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?
Answers
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.