Solve (1/2+b)*(-b+1/2)

$$( \frac { 1 } { 2 } + b ) \cdot ( - b + \frac { 1 } { 2 } )$$

Evaluate

$$\frac{1}{4}-b^{2}$$

Solution Steps

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

$$\frac{1}{2}\left(-b\right)+\frac{1}{2}\times \frac{1}{2}+b\left(-b\right)+b\times \frac{1}{2}$$

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

$$\frac{1}{2}\left(-b\right)+\frac{1\times 1}{2\times 2}+b\left(-b\right)+b\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

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

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

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

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

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

Combine -\frac{1}{2}b and b\times \frac{1}{2} to get 0.

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

Expand

$$\frac{1}{4}-b^{2}$$

Solution Steps

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

$$\frac{1}{2}\left(-b\right)+\frac{1}{2}\times \frac{1}{2}+b\left(-b\right)+b\times \frac{1}{2}$$

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

$$\frac{1}{2}\left(-b\right)+\frac{1\times 1}{2\times 2}+b\left(-b\right)+b\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

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

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

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

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

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

Combine -\frac{1}{2}b and b\times \frac{1}{2} to get 0.

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