Solve (-1/2a-b)(1/2a-b)

$$( - \frac { 1 } { 2 } a - b ) ( \frac { 1 } { 2 } a - b )$$

Evaluate

$$-\frac{a^{2}}{4}+b^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$-\frac{1}{4}a^{2}+\frac{1}{2}ab-b\times \frac{1}{2}a+b^{2}$$

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

$$-\frac{1}{4}a^{2}+\frac{1}{2}ab-\frac{1}{2}ba+b^{2}$$

Combine \frac{1}{2}ab and -\frac{1}{2}ba to get 0.

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

Expand

$$-\frac{a^{2}}{4}+b^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$-\frac{1}{4}a^{2}+\frac{1}{2}ab-b\times \frac{1}{2}a+b^{2}$$

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

$$-\frac{1}{4}a^{2}+\frac{1}{2}ab-\frac{1}{2}ba+b^{2}$$

Combine \frac{1}{2}ab and -\frac{1}{2}ba to get 0.

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