Expressions and Equations Part I

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a symbol that represents (stands for) a number Example: x or y
a number in front of a variable Example: 3x, the 3 is the coefficient
a number with no variable attached Example: 4, or in (w + 5), the 5 is a constant
variables, numbers, or the product of a number and variable(s) separated by addition or subtraction signs Example: One Term: x or 4y Two Terms: 3z + 2 Three Terms: 8w - 7t + 9
Algebraic Expression
A mathematical phrase that can contain numbers, variables and operations(+,-,x,÷) Examples: a + 1 or a - b or 3x
a number or variable with an exponent on it
Like Terms
Like Terms have the same variable base and exponent example: 3x and 6x
How to: Combine Like Terms
add the coefficients & keep the variables the same (do not + or - exponents) The sign in front of each term is part of the term 4y² + 7y² = 11y² You can't add 3x + 6x²
Distributive Property (with variables)
a(b+c) = a(b) + a(c) Always distribute before combining like terms Example: 6(2+4x) = 6(2) + 6(4x) = 12 + 24x
One Term Example: 3x
Two terms or monomials, connected through addition or subtraction Example: 3x - 6
Three terms or monomials, connected through addition or subtraction Example: 3x² - 6x + 4
an expression that is a monomial, binomial, trinomial, or larger
Adding Polynomials
Just like combining like terms Example: (3x² + 2x + 9) + (4x² + 6x - 1) = (7x² + 8x + 8)
Subtracting Polynomials
1 - Rewrite 1st polynomial 2 - Change subtraction to addition 3 - Change the signs of EVERY term in the 2nd polynomial 4 - Combine like terms (3x + 2xy + 7) - (6x - 4xy + 3) (3x + 2xy + 7) + (-6x + 4xy - 3) = -3x + 6xy + 4
To Find: Greatest Common Factor (GCF) Method 1
1) Completely factor each number (list all the factors) 2) The largest number they have in common is the answer
To Find: Greatest Common Factor (GCF) Method 2
1) Divide the numbers by any common factor 2) Check to see if the quotients can be divided by another common factor 3) Continue to divide by common factors until the only common factor is 1 4) The GCF will be the product of all the divisors (the common factors you divided by)
Use GCF to Factor Linear Expressions
6x + 18 1) Find the GCF of the coefficient & the constant GCF of 6 & 18 is 6 2) Divide the original problem by the GCF to get the second factor (6x+18) / 6 = x + 3 3) Write your answer as the product of the GCF & the Quotient 6(x + 3)
Using GCF to Factor Linear Expressions with Fractions
Use Rules for Using GCF to Factor Linear Expressions ***Differences: 1) change mixed numbers to improper fractions 2) need common denominators 3) find the GCF of the fractions (the gcf of the numerators over the common denominator) LOOK BACK AT YOUR NOTES, THIS IS TOUGH