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

### Answer & Explanation

Solution:

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

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

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

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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