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What is the coefficient of $x^2y^6$ in the expansion of $\left(\frac{3}{5}x-\frac{y}{2}\right)^8$? Express your answer as a common fraction
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Let's expand the expression \left(\frac{3}{5}x - \frac{1}{2}y\right)^8.
This is a binomial expansion of the form (a + b)^n where:
- a = \frac{3}{5}x
- b = -\frac{1}{2}y
- n = 8
We are looking for the coefficient of x^2y^6. This corresponds to the term where:
- x appears with power 2 → a^2
- y appears with power 6 → b^6
So we need the binomial term:
C(8, 2) * (3/5)^2 * (-1/2)^6
= 28 * (9/25) * (1/64)
= 28 * 9 / (25 * 64)
= 252 / 1600
= 63 / 400
FINAL_ANSWER: \frac{63}{400}
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how many a in banana?
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Let's count the number of 'a' in the word 'banana'.
The word 'banana' has the letters: b, a, n, a, n, a.
We see the letter 'a' appears 3 times.
FINAL_ANSWER: 3
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