Solve (3m^4-4m^3)^3

$$( 3 m ^ { 4 } - 4 m ^ { 3 } ) ^ { 3 }$$

Evaluate

$$\left(3m-4\right)^{3}m^{9}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(3m^{4}-4m^{3}\right)^{3}.

$$27\left(m^{4}\right)^{3}-108\left(m^{4}\right)^{2}m^{3}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$27m^{12}-108\left(m^{4}\right)^{2}m^{3}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$27m^{12}-108m^{8}m^{3}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$27m^{12}-108m^{11}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

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

$$27m^{12}-108m^{11}+144m^{4}m^{6}-64\left(m^{3}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$27m^{12}-108m^{11}+144m^{10}-64\left(m^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$27m^{12}-108m^{11}+144m^{10}-64m^{9}$$

Expand

$$27m^{12}-108m^{11}+144m^{10}-64m^{9}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(3m^{4}-4m^{3}\right)^{3}.

$$27\left(m^{4}\right)^{3}-108\left(m^{4}\right)^{2}m^{3}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$27m^{12}-108\left(m^{4}\right)^{2}m^{3}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$27m^{12}-108m^{8}m^{3}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$27m^{12}-108m^{11}+144m^{4}\left(m^{3}\right)^{2}-64\left(m^{3}\right)^{3}$$

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

$$27m^{12}-108m^{11}+144m^{4}m^{6}-64\left(m^{3}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$27m^{12}-108m^{11}+144m^{10}-64\left(m^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$27m^{12}-108m^{11}+144m^{10}-64m^{9}$$