Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.
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Transcript of Addition, Subtraction, and Multiplication Chapter 4 Sections 1-6.
Addition, Subtraction, and Multiplication
Chapter 4 Sections 1-6
Simplify the expression within the grouping symbols.
Then simplify powers.Then simplify products and quotients in order
from left to right.Then simplify sums and differences in order from
left to right.
In other words, follow the Acronym PEMDAS:Please Excuse My Dear Aunt Sally
Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction
Monomial - an expression that is either a number, a variable, or the product of a number and one or more variables
Polynomial - the sum of one or more monomials Binomial - a polynomial with two terms Trinomial - a polynomial with three terms
Coefficient - the numerical value being multiplied in front of the variable
Degree Monomial - the sum of the exponents of each variable Polynomial - the greatest of the degrees of a
polynomial’s terms after it has been simplified.
Line up the like terms of each polynomial, keeping the sign with each term.Like Terms – monomials with the same variables
raised to the same exponents
Add or subtract the coefficients of like terms, based on the sign of the term
2 35 4 3x x y 3 2 5 13x y
2 35 6 8 13x x y
2 411 2 4a b 2 4 (2 5 1)a b 2 49 7 5a b
Notice we subtract each term of the second polynomial.
“Popcorn rule” # 1: The Product of Powers
Same base means you add the exponents.
Examples:
m n m na a a
3 5x x 8x 2 45 3y y 615y
2 10 15 42 4a b a b 17 148a b
3x
Find the total surface area of this object.Remember: total surface area is the sum of the area of each face of the figure
x
xx
x
3x
Total Surface Area = 12•3x2 + 10•x2 = 46x2
Find the total surface area of this object.Remember: total surface area is the sum of the area of each face of the figure
The surface area of each “panel” or side face of the figure is 3x•x, or 3x2. There are 12 of these.
The area for 1 square of the top and bottom of the figure is x•x, or x2. There are 10 of these.
x
xx
x
x
3x
xx
“Popcorn rule” # 2: The Power of Powers
Two exponents next to each other means you multiply them.
Example:
“Popcorn rule” # 3: The Power of a Product
Raise each factor of the product to the power.
Example:
( )m n m na a
3 5( )x 15x
( )m m nab a b
2 3(5 )xy 3 6125x y