The number of terms in the expansion of ${[(a + 4 b)^{3} + (a - 4 b)^{3}]}^{2}$ are

6

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8

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7

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3

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Solution

The correct option is C $3$
$(x^{3} + y^{3})$
$= (x + y)^{3} - 3 x y (x + y)$
Applying the above formula on the given question we get
$[(a + 4 b)^{3} + (a - 4 b)^{3}]^{2}$
$= [8 a^{3} - 6 a (a^{2} - 16 b^{2})]^{2}$
$= [96 a b^{2} + 2 a^{3}]^{2}$
$= 4 a^{2} [48 b^{2} + a^{2}]^{2}$
$= 4 [2304 a^{2} b^{4} + 96 a^{4} b^{2} + a^{6}]$
Hence, the total number of terms is $3$ .

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The number of terms in the expansion of [(a+4b)3+(a−4b)3]2 are

The correct option is C 3(x3+y3)=(x+y)3−3xy(x+y)Applying the above formula on the given question we get[(a+4b)3+(a−4b)3]2=[8a3−6a(a2−16b2)]2=[96ab2+2a3]2=4a2[48b2+a2]2=4[2304a2b4+96a4b2+a6] Hence, the total number of terms is 3.

The number of terms in the expansion of ${[(a + 4 b)^{3} + (a - 4 b)^{3}]}^{2}$ are