Algebra Know-It-ALL

These rules also work for subtraction:

x(y−z)=xy−xz

and

(x−y)z=xz−yz

Variants of these rules work for division as long as the divisor (or denominator) consists of a
single nonzero variable, and never a sum or difference. Therefore

(x+y)/z=x/z+y /z

and

(x−y)/z=x /z−y /z

Zero numerator

For all nonzero real numbers x, if 0 is divided by x, then the quotient is equal to 0:

0/x= 0

Zero denominator

For all real numbers x, if x is divided by 0, then the quotient is undefined:

x /0 = (undefined)

Multiplication by zero

Whenever a real number x is multiplied by 0, the product is equal to 0:

x 0 = 0

and

0 x= 0

0th power

Whenever a nonzero real number x is taken to the 0th power, the result is equal to 1:

x^0 = 1 when x≠ 0

How Real Variables Behave 135