Solve (S-2t)(-S-2t)-(S-2t)^2

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

Evaluate

$$-2S\left(S-2t\right)$$

Solution Steps

Use the distributive property to multiply S-2t by -S-2t.

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

Multiply -2 and -1 to get 2.

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

Combine -2St and 2tS to get 0.

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

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

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

To find the opposite of S^{2}-4St+4t^{2}, find the opposite of each term.

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

Combine 4t^{2} and -4t^{2} to get 0.

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

Multiply S and S to get S^{2}.

$$S^{2}\left(-1\right)-S^{2}+4St$$

Combine S^{2}\left(-1\right) and -S^{2} to get -2S^{2}.

$$-2S^{2}+4St$$

Expand

$$4St-2S^{2}$$

Solution Steps

Use the distributive property to multiply S-2t by -S-2t.

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

Multiply -2 and -1 to get 2.

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

Combine -2St and 2tS to get 0.

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

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

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

To find the opposite of S^{2}-4St+4t^{2}, find the opposite of each term.

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

Combine 4t^{2} and -4t^{2} to get 0.

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

Multiply S and S to get S^{2}.

$$S^{2}\left(-1\right)-S^{2}+4St$$

Combine S^{2}\left(-1\right) and -S^{2} to get -2S^{2}.

$$-2S^{2}+4St$$