Solve 184(t^2-8)^3

$$184 ( t ^ { 2 } - 8 ) ^ { 3 }$$

Expand

$$184t^{6}-4416t^{4}+35328t^{2}-94208$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(t^{2}-8\right)^{3}.

$$184\left(\left(t^{2}\right)^{3}-24\left(t^{2}\right)^{2}+192t^{2}-512\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$184\left(t^{6}-24\left(t^{2}\right)^{2}+192t^{2}-512\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$184\left(t^{6}-24t^{4}+192t^{2}-512\right)$$

Use the distributive property to multiply 184 by t^{6}-24t^{4}+192t^{2}-512.

$$184t^{6}-4416t^{4}+35328t^{2}-94208$$

Evaluate

$$184\left(t^{2}-8\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(t^{2}-8\right)^{3}.

$$184\left(\left(t^{2}\right)^{3}-24\left(t^{2}\right)^{2}+192t^{2}-512\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$184\left(t^{6}-24\left(t^{2}\right)^{2}+192t^{2}-512\right)$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$184\left(t^{6}-24t^{4}+192t^{2}-512\right)$$

Use the distributive property to multiply 184 by t^{6}-24t^{4}+192t^{2}-512.

$$184t^{6}-4416t^{4}+35328t^{2}-94208$$