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A day full of math games & activities. Find one near you.
What is the third term in the binomial expansion of (3x + y3)4?
54x2y3
18x2y3
18x2y6
54x2y6
Solution:
Given, the expression is (3x + y3)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=y3 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 54x2y6
What is the third term in the binomial expansion of (3x + y3)4?
Summary:
The third term in the binomial expansion of (3x + y3)4 is 54x2y6.
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