Solve 36x^2(3x^2+4)^3

$$36 x ^ { 2 } ( 3 x ^ { 2 } + 4 ) ^ { 3 }$$

Expand

$$972x^{8}+3888x^{6}+5184x^{4}+2304x^{2}$$

Solution Steps

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

$$36x^{2}\left(27\left(x^{2}\right)^{3}+108\left(x^{2}\right)^{2}+144x^{2}+64\right)$$

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

$$36x^{2}\left(27x^{6}+108\left(x^{2}\right)^{2}+144x^{2}+64\right)$$

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

$$36x^{2}\left(27x^{6}+108x^{4}+144x^{2}+64\right)$$

Use the distributive property to multiply 36x^{2} by 27x^{6}+108x^{4}+144x^{2}+64.

$$972x^{8}+3888x^{6}+5184x^{4}+2304x^{2}$$

Evaluate

$$36x^{2}\left(3x^{2}+4\right)^{3}$$

Solution Steps

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

$$36x^{2}\left(27\left(x^{2}\right)^{3}+108\left(x^{2}\right)^{2}+144x^{2}+64\right)$$

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

$$36x^{2}\left(27x^{6}+108\left(x^{2}\right)^{2}+144x^{2}+64\right)$$

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

$$36x^{2}\left(27x^{6}+108x^{4}+144x^{2}+64\right)$$

Use the distributive property to multiply 36x^{2} by 27x^{6}+108x^{4}+144x^{2}+64.

$$972x^{8}+3888x^{6}+5184x^{4}+2304x^{2}$$