Expand the expression (2x^2-3y^3)^4

 Exercise

$\left(2x^2-3y^3\right)^4$

 

Expand the binomial $\left(2x^2-3y^3\right)^4$

$\left(2x^2\right)^4-12\left(2x^2\right)^3y^3+6\left(2x^2\right)^2\left(-3y^3\right)^2+8x^2\left(-3y^3\right)^3+\left(-3y^3\right)^4$

 

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

$16x^{8}-12\cdot 8x^{6}y^3+6\cdot 4x^{4}\left(-3y^3\right)^2+8x^2\left(-3y^3\right)^3+\left(-3y^3\right)^4$

 

Multiply $-12$ times $8$

$16x^{8}-96x^{6}y^3+6\cdot 4x^{4}\left(-3y^3\right)^2+8x^2\left(-3y^3\right)^3+\left(-3y^3\right)^4$

 

Multiply $6$ times $4$

$16x^{8}-96x^{6}y^3+24x^{4}\left(-3y^3\right)^2+8x^2\left(-3y^3\right)^3+\left(-3y^3\right)^4$

$16x^{8}-96x^{6}y^3+24x^{4}\left(-3y^3\right)^2+8x^2\left(-3y^3\right)^3+\left(-3y^3\right)^4$

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