Solve (9t^2-1)^3

$$( 9 t ^ { 2 } - 1 ) ^ { 3 }$$

Expand

$$729t^{6}-243t^{4}+27t^{2}-1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(9t^{2}-1\right)^{3}.

$$729\left(t^{2}\right)^{3}-243\left(t^{2}\right)^{2}+27t^{2}-1$$

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

$$729t^{6}-243\left(t^{2}\right)^{2}+27t^{2}-1$$

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

$$729t^{6}-243t^{4}+27t^{2}-1$$

Evaluate

$$\left(9t^{2}-1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(9t^{2}-1\right)^{3}.

$$729\left(t^{2}\right)^{3}-243\left(t^{2}\right)^{2}+27t^{2}-1$$

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

$$729t^{6}-243\left(t^{2}\right)^{2}+27t^{2}-1$$

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

$$729t^{6}-243t^{4}+27t^{2}-1$$