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State the coefficient of x^2 in (2x+1)^5

The answers section says that x^2 is the 4th term => r = 3
But I thought x^2 was the third term because x^0, x^1, x^2


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1 Answer

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Best answer

You normally write a polynomial with the powers in descending order, like this:

$$ax^5 + bx^4 + cx^3 + dx^2 + kx + m$$

There it is term 4. It shouldn't matter which way you count it though, because of the symmetry of Pascal's triangle (which is related to how the nCr numbers pop out).

The x^2 term (regardless of how you number it... 4 or 3...) is computed by:

(2x)^2 * (1)^3 * 5Cr

You'll notice that r=3 or r=2 depending on how you counted it. But 5C3 and 5C2 are the same!


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