Solve 16({left(-x/2right)}^2)+2(4x-3)(-x/2)-21

$$16( { \left( \frac{ -x }{ 2 } \right) }^{ 2 } )+2(4x-3)( \frac{ -x }{ 2 } )-21$$

Evaluate

$$3\left(x-7\right)$$

Solution Steps

To raise \frac{-x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$16\times \frac{\left(-x\right)^{2}}{2^{2}}+2\left(4x-3\right)\times \frac{-x}{2}-21$$

Express 16\times \frac{\left(-x\right)^{2}}{2^{2}} as a single fraction.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+2\left(4x-3\right)\times \frac{-x}{2}-21$$

Cancel out 2 and 2.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+\left(-x\right)\left(4x-3\right)-21$$

Use the distributive property to multiply -x by 4x-3.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+4\left(-x\right)x-3\left(-x\right)-21$$

Multiply -3 and -1 to get 3.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+4\left(-x\right)x+3x-21$$

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

$$\frac{16x^{2}}{2^{2}}+4\left(-x\right)x+3x-21$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16x^{2}}{4}+4\left(-x\right)x+3x-21$$

Divide 16x^{2} by 4 to get 4x^{2}.

$$4x^{2}+4\left(-x\right)x+3x-21$$

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

$$4x^{2}+4\left(-1\right)x^{2}+3x-21$$

Multiply 4 and -1 to get -4.

$$4x^{2}-4x^{2}+3x-21$$

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

$$3x-21$$

Expand

$$3x-21$$

Solution Steps

To raise \frac{-x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$16\times \frac{\left(-x\right)^{2}}{2^{2}}+2\left(4x-3\right)\times \frac{-x}{2}-21$$

Express 16\times \frac{\left(-x\right)^{2}}{2^{2}} as a single fraction.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+2\left(4x-3\right)\times \frac{-x}{2}-21$$

Cancel out 2 and 2.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+\left(-x\right)\left(4x-3\right)-21$$

Use the distributive property to multiply -x by 4x-3.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+4\left(-x\right)x-3\left(-x\right)-21$$

Multiply -3 and -1 to get 3.

$$\frac{16\left(-x\right)^{2}}{2^{2}}+4\left(-x\right)x+3x-21$$

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

$$\frac{16x^{2}}{2^{2}}+4\left(-x\right)x+3x-21$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16x^{2}}{4}+4\left(-x\right)x+3x-21$$

Divide 16x^{2} by 4 to get 4x^{2}.

$$4x^{2}+4\left(-x\right)x+3x-21$$

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

$$4x^{2}+4\left(-1\right)x^{2}+3x-21$$

Multiply 4 and -1 to get -4.

$$4x^{2}-4x^{2}+3x-21$$

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

$$3x-21$$