Variable Expressions and Equations

Question 1

What is PEMDAS?

Answer 1

It is the order of math operations in an expression:
1) P_arentheses
2) E_xponents
3) M_ultiplication or
D_Division
4) A_ddition or
S_ubtraction

Question 2

Are the following terms like terms?
2xy + 2xy² - 4x²y + x²y²

Answer 2

None of the terms are like terms. They all have different combinations of variables and exponents.

Question 3

Is the following equation true?

√2 + 3√2 = 1√2 + 3√2 = (1 + 3)√2 = 4√2

Answer 3

Yes. For the purposes of like terms, treat the square root of a number like a variable; the square root is the common factor

Question 4

Combine as many like terms as possible:

8ba + ab² - 5ab + ab² - 2ba²

Answer 4

(8ab - 5ab) + (ab² + ab²) + (-2a²b) =

3ab + 2ab² - 2a²b

Question 5

Distribute the expression below:
√2(1 - x√2)

Answer 5

√2 x (1 - x√2) =
(√2) x (1) + (√2) x (-x√2) =
√2 - 2x

Question 6

Factor the below expression:
4x² + 3xy - yx + 6x

Answer 6

4x² + 2xy + 6x =
2x (2x + y + 3)