What is the third term in the expansion of ${(cos x + 3)}^{5}$ $(cos x+3)^5$ ?

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What is the third term in the expansion of ${(cos x + 3)}^{5}$ $(cos x+3)^5$ ?

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Answer 1 · 2016-07-14T01:59:55

We use the formula $t_{k + 1} = {t w o}_{n} C_{k} {(x)}^{n - k} \times y^{k}$ $t_(k + 1)=color(white)(two)_nC_k(x)^(n - k) xx y^k$ , where ${t w o}_{n} C_{k}$ $color(white)(two)_nC_k$ denotes the combination formula in the context of ${(x + y)}^{n}$ $(x + y)^n$ .

Since we're looking for the third term, $k + 1 = 3 \to k = 2$ $k + 1 = 3 ->k = 2$ .

$t_{3} = {t w o}_{5} C_{2} \times {(cos x)}^{5 - 2} \times 3^{2}$ $t_3 = color(white)(two)_5C_2 xx (cosx)^(5 - 2) xx 3^2$

$t_{3} = \frac{5!}{(5 - 2)! \times 2!} \times {(cos x)}^{3} \times 9$ $t_3 = (5!)/((5 - 2)! xx 2!) xx (cosx)^3 xx 9$

$t_{3} = 10 \times {cos}^{3} x \times 9$ $t_3 = 10 xx cos^3x xx 9$

$t_{3} = 90 {cos}^{3} x$ $t_3 = 90cos^3x$

Hopefully this helps!

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What is the third term in the expansion of ${(cos x + 3)}^{5}$ $(cos x+3)^5$ ?

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