Part 2: Algebra Flashcards Preview

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Flashcards in Part 2: Algebra Deck (96)
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1

What is a variable?

A letter that represents an unknown value

2

What is an algebraic expression?

an arithmetic expression with one or more variables

3

What is a term?

It's a single part of an algebraic expression that is separated by an addition or subtraction sign from other parts of the expression.

4

What are like terms?

Terms are alike when they contain the same variables, with the same exponents.

5

What is a constant?

A term that does not contain any variables.

6

What is a coefficient?

A number that is multiplied by variables.

7

What is a polynomial?

An algebraic expression with a finite number of terms.

8

What is the degree of a term?

It's the exponent that's on the variable.

9

What is the degree of a polynomial?

The greatest exponent in the polynomial.

10

Identity 1: ca + cb

c(a + b)

11

Identity 2: ca - cb

c(a - b)

12

Identity 3: (a + b) ^2

a^2 + 2ab + b^2

13

Identity 4: (a - b)^2

a^2 - 2ab + b^2

14

Identity 5: a^2 - b^2

(a + b)(a - b)

15

Identity 6: (a + b) ^3

a^3 + 3a^2b + 3ab^2 + b^3

16

Identity 7: (a - b)^3

a^3 - 3a^2b + 3ab^2 - b^3

17

Rule 1: x^-a

1/x^a

18

Rule 2: (x^a)(x^b)

x^(a+b)

19

Rule 3a: x^a/x^b

x^(a-b)

20

Rule 3b: x^(a-b)

1/x^(b-a)

21

Rule 4: x^0

1

22

Rule 5: (x^a)(y^a)

(xy)^a

23

Rule 6: (x/y)^a

(x^a)/(y^a)

24

Rule 7: (x^a)^b

x^(ab)

25

What is an equation?

It is a statement of equality between two expressions.

26

What does it mean to solve an equation?

It means to find the values of the variables that satisfy the equation.

27

What are equivalent equations?

They are equations that have the same solution.

28

Equivalent equation rule #1 regarding constants:

The same constant can be added or substracted from each side of an equation, equality is preserved and the new equation is equivalent to the old one.

29

Equivalent equation rule #2 regarding constants:

The same constant can be multiplied or divided on each side of an equation and the new equation will be equivalent to the original one.

30

Equivalent equation rule #3 regarding equivalent expressions:

An equivalent expression can replace an expression inside an equation and the new equation will be equivalent to the original one.