WEBVTT
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Find the second-to-last term in two plus π₯ all raised to the power of 34.
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In order to answer this question, we need to recall the binomial expansion of π plus π to the πth power, where π is a natural number, as shown.
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The general term is equal to π choose π multiplied by π to the power of π minus π multiplied by π to the power of π, where π choose π is equal to π factorial divided by π minus π factorial multiplied by π factorial.
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We are asked to calculate the second-to-last term.
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This is equal to π choose π minus one multiplied by π to the power of one multiplied by π to the power of π minus one.
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In this question, π is equal to two, π is equal to π₯, and the exponent π equals 34.
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This means we need to calculate 34 choose 33 multiplied by two to the power of one multiplied by π₯ to the power of 34 minus one.
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34 choose 33 is equal to 34 factorial divided by one factorial multiplied by 33 factorial.
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We can rewrite the numerator as 34 multiplied by 33 factorial.
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And as one factorial equals one, the denominator is 33 factorial.
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Dividing the numerator and denominator by 33 factorial gives us 34.
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The second-to-last term simplifies to 34 multiplied by two multiplied by π₯ to the power of 33.
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This is equal to 68π₯ to the power of 33.