Flashcards in Algebraic Expressions Deck (27):
What is a variable?
A variable is an unspecified number that is represented with a letter of the alphabet. It is the unknown in an algebraic expression.
What is the coefficient?
The coefficient is the number that the base is being multiplied by.
What is the base?
The base is the number that has an exponent.
What is the power?
The power is the exponent.
How do we write algebraic expressions?
The coefficient comes first, then the bases in alphabetical order.
What is the first exponent law?
When we multiply the same base we add exponents.
Bases must be the same to add the exponents.
What is the second exponent law?
When we divide the same bases, we subtract exponents.
When a number or variable appears in both the numerator and the denominator, we can 'cancel' the number or variable
What is the third exponent law?
When you raise a power to a power you multiply exponents.
When you have two bases, multiply both exponents for each base separately.
Anything divided by anything must still be relevant to the power.
Make sure you apply the exponent to the coefficient in the bracket.
What is the fourth exponent law?
Anything (except zero) to the power of zero can be replaced with one.
What is a term?
A term is a series of numbers and operations. Different terms are separated by plus or minus signs. Anything in a bracket is a single term.
What is a monomial?
An expression with a single term.
What is a binomial?
An expression with two terms.
What is a trinomial?
An expression with three terms.
What is a polynomial?
An expression with four or more terms.
What must we do when we multiply in algebra?
Simplify the sum first.
What must we do when we divide in algebra?
Simplify the sum
Handle the numerator and denominator separately, then divide.
What is important to remember in algebra?
What must we do when simplifying algebraic expressions?
1. Determine the signs
2. Multiply or divide the coefficients
3. Multiply or divide the variables
What happens when we add variables in algebra?
Only add like terms. The same goes for subtraction.
What is important to remember about variables with no coefficients?
The coefficient is actually 1. So if we add two like terms with no apparent coefficient, the answer will be 2a; 2b; 2c, etc.
What is important to remember when dividing exponents where the exponent in the denominator is larger than the one in the numerator?
The higher exponent stays in the denominator. So if we have 2asquared in the numerator, and 4acubed in the denominator, the answer will be 1 over 2a, because the higher exponent stays in the denominator.
What happens when we multiply or divide unlike terms?
We can still multiply or divide them. The law about like terms only applies to addition and subtraction.
What happens when we are dividing and there are more terms in the numerator than in the denominator?
We can split up the numerator into its separate terms and place each of them over the denominator.
What happens when there is no visible exponent?
The exponent will be 1.
What method can be used to multiply a monomial, a binomial or any polynomial containing a variable with a number outside a bracket?
For instance 5(6+a)
The distributive method.
For instance 5(6+a)
Can be split into 5(6)+5(a)
What is a constant?
A constant is a number the value of which does not change. If there is no known constant, the constant is plus 0.