Solve (a-1)*(a-1/100)-a(a-101/100)

$$( a - 1 ) \times ( a - \frac { 1 } { 100 } ) - a ( a - \frac { 101 } { 100 } )$$

Evaluate

$$\frac{1}{100}=0.01$$

Solution Steps

Apply the distributive property by multiplying each term of a-1 by each term of a-\frac{1}{100}.

$$a^{2}+a\left(-\frac{1}{100}\right)-a-\left(-\frac{1}{100}\right)-a\left(a-\frac{101}{100}\right)$$

Combine a\left(-\frac{1}{100}\right) and -a to get -\frac{101}{100}a.

$$a^{2}-\frac{101}{100}a-\left(-\frac{1}{100}\right)-a\left(a-\frac{101}{100}\right)$$

Multiply -1 and -\frac{1}{100} to get \frac{1}{100}.

$$a^{2}-\frac{101}{100}a+\frac{1}{100}-a\left(a-\frac{101}{100}\right)$$

Use the distributive property to multiply a by a-\frac{101}{100}.

$$a^{2}-\frac{101}{100}a+\frac{1}{100}-\left(a^{2}+a\left(-\frac{101}{100}\right)\right)$$

To find the opposite of a^{2}+a\left(-\frac{101}{100}\right), find the opposite of each term.

$$a^{2}-\frac{101}{100}a+\frac{1}{100}-a^{2}-a\left(-\frac{101}{100}\right)$$

Multiply -1 and -\frac{101}{100} to get \frac{101}{100}.

$$a^{2}-\frac{101}{100}a+\frac{1}{100}-a^{2}+\frac{101}{100}a$$

Combine a^{2} and -a^{2} to get 0.

$$-\frac{101}{100}a+\frac{1}{100}+\frac{101}{100}a$$

Combine -\frac{101}{100}a and \frac{101}{100}a to get 0.

$$\frac{1}{100}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5 ^ {2}} = 0.01$$

Solution Steps

Factor out \frac{1}{100}.

$$\frac{\left(a-1\right)\left(100a-1\right)-a\left(100a-101\right)}{100}$$