Solve (3x^4+4x^3)^3

$$( 3 x ^ { 4 } + 4 x ^ { 3 } ) ^ { 3 }$$

Evaluate

$$\left(3x+4\right)^{3}x^{9}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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