Expand the expression (1/3x^3-2/5x^2)^2

 Exercise

$\left(\frac{1}{3}x^3-\frac{2}{5}x^2\right)^2$

 

Expand $\left(\frac{1}{3}x^3-\frac{2}{5}x^2\right)^2$

$\left(\frac{1}{3}x^3\right)^2+\frac{2}{3}\cdot -\frac{2}{5}x^3x^2+\left(-\frac{2}{5}x^2\right)^2$

 

When multiplying exponents with same base we can add the exponents

$\left(\frac{1}{3}x^3\right)^2+\frac{2}{3}\cdot \left(-\frac{2}{5}\right)x^{5}+\left(-\frac{2}{5}x^2\right)^2$

 

The power of a product is equal to the product of it's factors raised to the same power

$\frac{1}{9}x^{6}+\frac{2}{3}\cdot -\frac{2}{5}x^{5}+\left(-\frac{2}{5}x^2\right)^2$

 

Multiplying fractions $\frac{2}{3} \times -\frac{2}{5}$

$\frac{1}{9}x^{6}-\frac{4}{15}x^{5}+\left(-\frac{2}{5}x^2\right)^2$

$\frac{1}{9}x^{6}-\frac{4}{15}x^{5}+\left(-\frac{2}{5}x^2\right)^2$

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