Question

Find the coefficient ofx^7 in the expression (x^3+\frac{4}{x^2})^4

Ratios, rates, proportions
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asked 2021-05-14
Find the coefficient of\(x^7\) in the expression \((x^3+\frac{4}{x^2})^4\)

Answers (1)

2021-05-15
Solution:
\((x^3+\frac{4}{x^2})^4=((x^3+\frac{4}{x^2})^2)\)
\(=(x^6+\frac{16}{x^4}+8x)^2\)
\(=x^{12}+\frac{256}{x^8}+64x^2+2[x^6\cdot\frac{16}{x^4}+x^6\cdot8x+\frac{16}{x^4}\cdot8x]\)
So: \((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)\)
Required form =8x
Coefficient \(x^2=8\)
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