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

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

Evaluate

$$-\frac{5ab}{2}+a^{2}+b^{2}$$

Solution Steps

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

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

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

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

Cancel out 2 and 2.

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

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

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

Combine -\frac{1}{2}ab and -2ba to get -\frac{5}{2}ab.

$$a^{2}-\frac{5}{2}ab+b^{2}$$

Expand

$$-\frac{5ab}{2}+a^{2}+b^{2}$$

Solution Steps

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

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

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

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

Cancel out 2 and 2.

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

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

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

Combine -\frac{1}{2}ab and -2ba to get -\frac{5}{2}ab.

$$a^{2}-\frac{5}{2}ab+b^{2}$$