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# What is the third term in the binomial expansion of (3x + y^{3})^{4}?

54x^{2}y^{3}

18x^{2}y^{3}

18x^{2}y^{6 }

54x^{2}y^{6}

**Solution:**

Given, the expression is (3x + y^{3})^{4}

We have to find the third term in the binomial expansion.

The general formula for binomial expansion is

\(a^{n}+na^{n-1}b+\frac{n(n-1)}{2}a^{n-2}b^{2}+............+b^{n}\)

Here, a=3x, b=y^{3} and n=4

Substituting the values in the formula,

\(3x^{4}+4(3x)^{4-1}y^{3}+\frac{(4)(4-1)}{2}3x^{4-2}(y^{3})^{2}+............\\(3x)^{4}+4(3x)^{3}y^{3}+6(3x)^{2}y^{6}+................\\81x^{4}+108x^{3}y^{3}+54x^{2}y^{6}+.....\)

Therefore, the third term is 54x^{2}y^{6}

## What is the third term in the binomial expansion of (3x + y^{3})^{4}?

**Summary:**

The third term in the binomial expansion of (3x + y^{3})^{4} is 54x^{2}y^{6}.

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