Solve (1/2x+2)*(4x-1/2)

$$( \frac { 1 } { 2 } x + 2 ) \times ( 4 x - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{\left(8x-1\right)\left(x+4\right)}{4}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}x+2 by each term of 4x-\frac{1}{2}.

$$\frac{1}{2}x\times 4x+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

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

$$\frac{1}{2}x^{2}\times 4+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}x^{2}+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

Divide 4 by 2 to get 2.

$$2x^{2}+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$2x^{2}+\frac{1\left(-1\right)}{2\times 2}x+8x+2\left(-\frac{1}{2}\right)$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 2}.

$$2x^{2}+\frac{-1}{4}x+8x+2\left(-\frac{1}{2}\right)$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$2x^{2}-\frac{1}{4}x+8x+2\left(-\frac{1}{2}\right)$$

Combine -\frac{1}{4}x and 8x to get \frac{31}{4}x.

$$2x^{2}+\frac{31}{4}x+2\left(-\frac{1}{2}\right)$$

Cancel out 2 and 2.

$$2x^{2}+\frac{31}{4}x-1$$

Expand

$$2x^{2}+\frac{31x}{4}-1$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{2}x+2 by each term of 4x-\frac{1}{2}.

$$\frac{1}{2}x\times 4x+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

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

$$\frac{1}{2}x^{2}\times 4+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}x^{2}+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

Divide 4 by 2 to get 2.

$$2x^{2}+\frac{1}{2}x\left(-\frac{1}{2}\right)+8x+2\left(-\frac{1}{2}\right)$$

Multiply \frac{1}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$2x^{2}+\frac{1\left(-1\right)}{2\times 2}x+8x+2\left(-\frac{1}{2}\right)$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 2}.

$$2x^{2}+\frac{-1}{4}x+8x+2\left(-\frac{1}{2}\right)$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$2x^{2}-\frac{1}{4}x+8x+2\left(-\frac{1}{2}\right)$$

Combine -\frac{1}{4}x and 8x to get \frac{31}{4}x.

$$2x^{2}+\frac{31}{4}x+2\left(-\frac{1}{2}\right)$$

Cancel out 2 and 2.

$$2x^{2}+\frac{31}{4}x-1$$