# What is the coefficient of the x^{5}y^{5}-term in the binomial expansion of (2x - 3y)^{10}?

**Solution:**

The given binomial expansion is (2x - 3y)^{10} --- (1)

The general form of binomial expansion is (a + b)^{n} --- (2)

Comparing (1) and (2)

a = 2x, b = -3y, n = 10

We have to find the coefficient of the term x^{5}y^{5}

This implies r = 5

The terms in the expansion can be obtained using

\(T_{r+1}=\, ^{n}C_{r}a^{(n-r)}b^{r}\)

Now, \(\\T_{5+1}=\, ^{10}C_{5}(2x)^{(10-5)}(-3y)^{5}\\T_{6}=\, ^{10}C_{5}(2x)^{5}(-3y)^{5}\\T_{6}=\, ^{10}C_{5}(2)^{5}x^{5}(-3)^{5}(y)^{5}\\T_{6}=\, ^{10}C_{5}(2)^{5}(-3)^{5}x^{5}y^{5}\)

Therefore, the coefficient of the term \(x^{5}y^{5}=\, ^{10}C_{5}(2)^{5}(-3)^{5}\).

## What is the coefficient of the x^{5}y^{5}-term in the binomial expansion of (2x - 3y)^{10}?

**Summary:**

The coefficient of the x^{5}y^{5}-term in the binomial expansion of (2x - 3y)^{10} is \(\, ^{10}C_{5}(2)^{5}(-3)^{5}\).

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