Algebraic Expressions

Question 1

What is a variable?

Answer 1

A variable is an unspecified number that is represented with a letter of the alphabet. It is the unknown in an algebraic expression.

Question 2

What is the coefficient?

Answer 2

The coefficient is the number that the base is being multiplied by.

Question 3

What is the base?

Answer 3

The base is the number that has an exponent.

Question 4

What is the power?

Answer 4

The power is the exponent.

Question 5

How do we write algebraic expressions?

Answer 5

The coefficient comes first, then the bases in alphabetical order.

Question 6

What is the first exponent law?

Answer 6

When we multiply the same base we add exponents.

Bases must be the same to add the exponents.

Question 7

What is the second exponent law?

Answer 7

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

Question 8

What is the third exponent law?

Answer 8

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.

Question 9

What is the fourth exponent law?

Answer 9

Anything (except zero) to the power of zero can be replaced with one.

Question 10

What is a term?

Answer 10

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.

Question 11

What is a monomial?

Answer 11

An expression with a single term.

Question 12

What is a binomial?

Answer 12

An expression with two terms.

Question 13

What is a trinomial?

Answer 13

An expression with three terms.

Question 14

What is a polynomial?

Answer 14

An expression with four or more terms.

Question 15

What must we do when we multiply in algebra?

Answer 15

Simplify the sum first.

Question 16

What must we do when we divide in algebra?

Answer 16

Simplify the sum

Handle the numerator and denominator separately, then divide.

Question 17

What is important to remember in algebra?

Answer 17

B
E
D
M
A
S

Question 18

What must we do when simplifying algebraic expressions?

Answer 18

1. Determine the signs
2. Multiply or divide the coefficients
3. Multiply or divide the variables

Question 19

What happens when we add variables in algebra?

Answer 19

Only add like terms. The same goes for subtraction.

Question 20

What is important to remember about variables with no coefficients?

Answer 20

The coefficient is actually 1. So if we add two like terms with no apparent coefficient, the answer will be 2a; 2b; 2c, etc.

Question 21

What is important to remember when dividing exponents where the exponent in the denominator is larger than the one in the numerator?

Answer 21

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.

Question 22

What happens when we multiply or divide unlike terms?

Answer 22

We can still multiply or divide them. The law about like terms only applies to addition and subtraction.

Question 23

What happens when we are dividing and there are more terms in the numerator than in the denominator?

Answer 23

We can split up the numerator into its separate terms and place each of them over the denominator.

Question 24

What happens when there is no visible exponent?

Answer 24

The exponent will be 1.

Question 25

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)

Answer 25

The distributive method.
For instance 5(6+a)
Can be split into 5(6)+5(a)
30+5a

Question 26

What is a constant?

Answer 26

A constant is a number the value of which does not change. If there is no known constant, the constant is plus 0.

Question 27

What is substitution?

Answer 27

Substitution is when you replace the variable in an expression with a value and figure out what the result would be if the variable was that value.