Explained: "Find the coefficient ofx7 in the expression (x3+4x2)4"

boitshupoO

Answered question

2021-05-14

Find the coefficient of

x^{7}

in the expression

(x^{3} + \frac{4}{x^{2}})^{4}

Delorenzoz

Skilled2021-05-15Added 91 answers

Solution:

(x^{3} + \frac{4}{x^{2}})^{4} = ((x^{3} + \frac{4}{x^{2}})^{2})

= (x^{6} + \frac{16}{x^{4}} + 8 x)^{2}

= x^{12} + \frac{256}{x^{8}} + 64 x^{2} + 2 [x^{6} \cdot \frac{16}{x^{4}} + x^{6} \cdot 8 x + \frac{16}{x^{4}} \cdot 8 x]

So:

(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 (a b + b c + a c)

Required form =8x
Coefficient

x^{2} = 8

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