Algebra
Algebra Vocabulary Algebraic Expression- a math sentence involving a variable or unknown Variable- a symbol for a letter we don’t know yet Constant- a number on its own Coefficient- a number used to multiply a variable Operator- a symbol that shows an operation Like Terms- are terms whose variables (and their exponents) are the same. In other words, terms that are "like" each other. (Note: the coefficients can be different) Polynomial- an equation that has constants, variables and the exponents; NEVER DIVISION
Rules You can only combine like terms Signs (+/-) are attached to the coefficient and variable - (-) = + Positive + Positive = Positive Positive + Negative = the sign of the larger digit Negative – Negative = the sign of the larger number Negative – Positive = negative Positive x Positive = Positive Positive x Negative = Negative Negative x Negative = Positive Positive Positive = Positive Negative Negative = Positive Negative Positive = Negative Positive Negative = Negative
Operation Key Words Addition: sum, total, plus, in all, all together, and, increased by Subtraction: difference, less than, fewer, from, take away, are not, remain, how many more, exceed, remain Multiplication: times, each, in all, twice, product, factor, multiple, multiplied by Division: same, split, equal groups, separate, shared equally, distribute, cut up
Take away 6 from 5 times of g Write an expression Identify the variable Look for key words Identify the operations Example: Take away 6 from 5 times of g Subtract and Multiply Answer: 5g-6
Write an expression 5 more than quotient of x and 3 Addition and Division 5 + x/3 9 less than 8 times of y Subtraction and Multiplication 8y-9 Add 2 times of k and one-third Addition and Multiplication 2 + 1k/3
Writing and Expression Product of 5 and y Quotient of 6 and a Take away 2 from q 4 is added to p 3 times of x One-half of q is added to 7 Two-third of the sum of 5 and m Six-fifth of h is subtracted from 3 5 less than quotient of w and 7 9 minus h
Adding Polynomials Line up like terms (this may involve re-arranging) 2x2 + 3xy+4 3x2+5xy+2 Add down the columns (Add like terms) 3x2+ 5xy +2 Note: the only aspect that changes is the coefficient Answer: 5x2+ 8xy + 6
Adding Polynomials
Adding Polynomials
Subtracting Polynomials Line up like terms (this may involve re-arranging) 2x2 + 3xy+4 3x2+5xy+2 Multiply all terms in the second polynomial by -1 3x2+5xy+2 -3x2- 5xy -2 Add down the columns (Add like terms) 2x2 + 3xy +4 -3x2- 5xy -2 Note: the only aspect that changes is the coefficient Answer: -1x2-2xy + 2
Subtracting Polynomials
Subtracting Polynomials