Solve (t^2-2t)^2

$$( t ^ { 2 } - 2 t ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

$$\left(t^{2}\right)^{2}-4t^{2}t+4t^{2}$$

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

$$t^{4}-4t^{2}t+4t^{2}$$

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

$$t^{4}-4t^{3}+4t^{2}$$

Expand

$$t^{4}-4t^{3}+4t^{2}$$

Solution Steps

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

$$\left(t^{2}\right)^{2}-4t^{2}t+4t^{2}$$

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

$$t^{4}-4t^{2}t+4t^{2}$$

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

$$t^{4}-4t^{3}+4t^{2}$$