The numbers of non-zero terms in the expansion of (1+32x)9+(1−32x)9 is:

(1+32x)9+(1−32x)9=2 9C0+9C2(32x)2+9C4(32x)4+⋯+9C8(32x)8∴number of non-zero terms =5

The numbers of non-zero terms in the expansion of (1+32x)9+(1−32x)9 is:

(1+32x)9+(1−32x)9=2 9C0+9C2(32x)2+9C4(32x)4+⋯+9C8(32x)8∴number of non-zero terms =5

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The numbers of non-zero terms in the expansion of ${(1 + 3 \sqrt{2} x)}^{9} + {(1 - 3 \sqrt{2} x)}^{9}$ is:

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Detailed Solution

$\begin{array}{l} {(1 + 3 \sqrt{2} x)}^{9} + {(1 - 3 \sqrt{2} x)}^{9} \\ = 2 [^{9} C_{0} +^{9} C_{2} {(3 \sqrt{2} x)}^{2} +^{9} C_{4} {(3 \sqrt{2} x)}^{4} + \dots +^{9} C_{8} {(3 \sqrt{2} x)}^{8}] \end{array}$

$∴$ number of non-zero terms $= 5$

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