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Number of Terms in Binomial Expansion

The number of...

Question

The number of terms in the expansion of ${(9 x^{2} + 12 x + 4)}^{30}$ is

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Solution

${(9 x^{2} + 12 x + 4)}^{30}$
$\Rightarrow 9 x^{2} + 12 x + 4 = (2 + 3 x)^{2}$
${(9 x^{2} + 12 x + 4)}^{30} = {((2 + 3 x)^{2})}^{30}$
$\Rightarrow (2 + 3 x)^{60}$
Here, $n = 60$ , we know that number of terms in the binomial expansion is $n + 1 = 61$

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