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What is the fourth term in the binomial expansion (a+b)^6)

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7 votes

Answer:


20a^3b^3

Explanation:

Binomial Series


(a+b)^n=a^n+(n!)/(1!(n-1)!)a^(n-1)b+(n!)/(2!(n-2)!)a^(n-2)b^2+...+(n!)/(r!(n-r)!)a^(n-r)b^r+...+b^n

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:


\implies (n!)/(3!(n-3)!)a^(n-3)b^3


\implies (6!)/(3!(6-3)!)a^(6-3)b^3


\implies (6!)/(3!3!)a^(3)b^3


\implies \left((6 * 5 * 4 * \diagup\!\!\!\!3 * \diagup\!\!\!\!2 * \diagup\!\!\!\!1)/(3 * 2 * 1 * \diagup\!\!\!\!3 * \diagup\!\!\!\!2 * \diagup\!\!\!\!1)\right)a^(3)b^3


\implies \left((120)/(6)\right)a^(3)b^3


\implies 20a^3b^3

User Yogesh Chawla
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