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

 Exercise

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

 

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

$\left(\frac{1}{5}xy\right)^2-2xyx^2y^2+\left(-5x^2y^2\right)^2$

 

When multiplying exponents with same base you can add the exponents: $-2xyx^2y^2$

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

 

When multiplying exponents with same base you can add the exponents: $-2x^{3}y\cdot y^2$

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

 

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

$\frac{1}{25}x^2y^2-2x^{3}y^{3}+x^{4}\left(-5y^2\right)^2$

$\frac{1}{25}x^2y^2-2x^{3}y^{3}+x^{4}\left(-5y^2\right)^2$

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