Solve left(12^2x-6x^2right)^2

$${ \left( { 12 }^{ 2 } x-6 { x }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$36\left(x\left(24-x\right)\right)^{2}$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\left(144x-6x^{2}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(144x-6x^{2}\right)^{2}.

$$20736x^{2}-1728xx^{2}+36\left(x^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$20736x^{2}-1728x^{3}+36\left(x^{2}\right)^{2}$$

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

$$20736x^{2}-1728x^{3}+36x^{4}$$

Expand

$$36x^{4}-1728x^{3}+20736x^{2}$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\left(144x-6x^{2}\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(144x-6x^{2}\right)^{2}.

$$20736x^{2}-1728xx^{2}+36\left(x^{2}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$20736x^{2}-1728x^{3}+36\left(x^{2}\right)^{2}$$

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

$$20736x^{2}-1728x^{3}+36x^{4}$$