Solve (-z+2)^2-2z(-3z+4z)

$$( - z + 2 ) ^ { 2 } - 2 z ( - 3 z + 4 z )$$

Evaluate

$$4-4z-z^{2}$$

Solution Steps

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

$$\left(-z\right)^{2}+4\left(-z\right)+4-2z\left(-3z+4z\right)$$

Calculate -z to the power of 2 and get z^{2}.

$$z^{2}+4\left(-z\right)+4-2z\left(-3z+4z\right)$$

Combine -3z and 4z to get z.

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

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

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

Combine z^{2} and -2z^{2} to get -z^{2}.

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

Multiply 4 and -1 to get -4.

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

Expand

$$4-4z-z^{2}$$

Solution Steps

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

$$\left(-z\right)^{2}+4\left(-z\right)+4-2z\left(-3z+4z\right)$$

Calculate -z to the power of 2 and get z^{2}.

$$z^{2}+4\left(-z\right)+4-2z\left(-3z+4z\right)$$

Combine -3z and 4z to get z.

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

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

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

Combine z^{2} and -2z^{2} to get -z^{2}.

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

Multiply 4 and -1 to get -4.

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