ALGEBRA
4.1: Exponents (pgs: 136-142)
4.3: Multiplying Monomials (pgs: 148-150)
4.5: Multiplying a Polynomial by a Monomial (pgs: 154-156)
4.6: Multiplying Two Polynomials (pgs: 157-160)
4.4: Powers of Monomials (pgs: 151-153)
4.2: Adding and Subtracting Polynomials (pgs: 143-147)
The exponent indicates the number of times the base occurs as a factor
exponential form
factored form
2 cubed
2 x 2 x 2
In order to solve an expression/formula with exponents you have to follow the Order of Operations
PEMDAS: Parenthesis Exponents Multiplication Division Additon Subtraction
Polynomials: sum of monomials
Monomials: An expression that is either numeral, a variable, or a product of a numeral and one or more variables.
Binomials: two terms
Trinomial: three terms
7
h
1/2c
4x + 9
5b + 3ab + a
coefficient: The number at the side of a variable
8a
Like Terms: Two monomials that are exactly alike
-4x + 5x
Here the x is the like term
In an equation, only like terms can be added/subtracted/multiplied/divided
Degree of a Monomial: Is the total number of times its variables occurs as factors
-3xy2z3
1 in x
2 in y
3 in z
Degree of a Polynomial: Is the greatest of the degrees of its terms after it has been simplified
Subtracting Polynomials is very much like subtracting real numbers. To subtract a number you add the opposite of that number. To subtract a polynomial you add the opposite of each term of the polynomial that you are subtracting and then simplify.
Whenever you add a polynomial, you add first the coefficients and then the variable with its exponent stays the same (exponents are NOT added)
When you're multiplying monomials and you have two powers with the same base, you add the exponents
x2 + x8 = x(2+8) = x10
When you're multiplying a Polynomial by a Monomial you need to use Distributive Property and multiply the monomial by all the monomials into the polynomial
Distributive Property: To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more polynomials by a number(monomial) will give the same result as multiplying each polynomial individually by the number(monomial) and then adding the products together.
5(a + 2) = (5 x a) + (5 x 2 ) = 5a + 10 = 15a
When multiplying two polynomials you have to do the same as when adding a monomial by a polynomial. All you have to use is distributive property
(4x + 3)(3x + 4) = 4x**(3x + 4) + 3(3x + 4)* = 12x2 + 16x + 9x + 12 = 12x2 + 25x* + 12
Remember that the final answer keeps being an expression since they're NOT like terms