Expand the expression (4a^3-5b^2)^4

 Exercise

$\left(4a^3-5b^2\right)^4$

 

Expand the binomial $\left(4a^3-5b^2\right)^4$

$\left(4a^3\right)^4-20\left(4a^3\right)^3b^2+6\left(4a^3\right)^2\left(-5b^2\right)^2+16a^3\left(-5b^2\right)^3+\left(-5b^2\right)^4$

 

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

$256a^{12}-20\cdot 64a^{9}b^2+6\cdot 16a^{6}\left(-5b^2\right)^2+16a^3\left(-5b^2\right)^3+\left(-5b^2\right)^4$

 

Multiply $-20$ times $64$

$256a^{12}-1280a^{9}b^2+6\cdot 16a^{6}\left(-5b^2\right)^2+16a^3\left(-5b^2\right)^3+\left(-5b^2\right)^4$

 

Multiply $6$ times $16$

$256a^{12}-1280a^{9}b^2+96a^{6}\left(-5b^2\right)^2+16a^3\left(-5b^2\right)^3+\left(-5b^2\right)^4$

$256a^{12}-1280a^{9}b^2+96a^{6}\left(-5b^2\right)^2+16a^3\left(-5b^2\right)^3+\left(-5b^2\right)^4$

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.