Distributive Law, Like Terms, Exponent Laws Review

Distributive Law

Distributive Law is a rule that dictates that if a value is multiplied to a polynomial, it must be multiplied to every single value within the polynomial.

Example:

3(x + y)

= 3x + 3y

In this example, the value 3 is multiplied to polynomial x + y. As you can see it was multiplied to both x and y to find the answer. You would not multiply it to only x or only y and get an equations such as 3x +y. The monomial on the outside is distributed to every value within the brackets, hence the name. This remains true no matter how many numbers their are within the brackets.

Like Terms

Like terms are basically just terms with the same variables to the same power and are important when adding and subtracting. An example of a pair of like terms would be something like x and 2x. Both terms have the variable x and no other variables, making them like terms (Keep in mind that x is the same as 1x). Be cause they are like terms, x and 2x can be added or subtracted with each other, but other terms such as y or a term lacking any variables could not.

Example:

x^2 + x + 2x + y + 1 = x^2 + 3x + y + 1

In the example, the like terms x and 2x were added while x^2, y, and 1 were left untouched. Although x^2 shares the same variable with x and 2x, it has been raised to the power of 2, therefore making them not like terms. The other two values do not share the same variables (Or lack of variables) with any other terms in the question and therefore cannot be operated on further.

Exponent Laws

Exponent laws dictate how exponents behave in the context of certain operations. By grade 10, you should know at least 5 exponent laws. They are as follows:

Product Law: (a^m)(a^n) = a^(m + n)

Quotient Law: a^m/a^n = a^(m - n)

0 Exponent Law: a^0 = 1

Power of a Power Law: (a^m)^n = a^mn

Negative Exponent Law: a^-m = 1/a^m

In reality there are more, but they will not be necessary at this level. These laws should always be kept in mind while doing algebra involving exponents and will be necessary when doing calculus in the future.