This means that you multiply the variables two at a time from each of the two parts of the equation in the parentheses in this order:

First - Outside - Inside - Last

(2x - 3y)² =

(2x - 3y)(2x - 3y)

So, the first variables in each set of parentheses are 2x and 2x

FIRST: 2x ´ 2x = 4x²

The variables on the outside of each set of parentheses are 2x and 3y

OUTSIDE: 2x ´ -3y = - 6xy

The variables on the inside of each set of parentheses are -3y and 2x

INSIDE: -3y ´ 2x = - 6xy

The last variables in each set of parentheses are -3y and -3y

LAST: - 3y ´ - 3y = 9y²

Then we add all of the above parts together to get:

4x² - 6xy - 6xy + 9y² =

4x² + 9y² - 12xy

Example 2:

Algebra questions on the Accuplacer will also include inequalities problems. Inequalities contain the less than or greater than signs.

31 - 2/3X > 27, then X <

Solution 2:

In order to solve inequalities, deal with the whole numbers on each side of the equation first:

31 - 2/3X > 27 =

(31 - 31) - 2/3X > (27 - 31) =

- 2/3X > - 4

Then deal with the fraction:

- 2/3X > - 4 =

3 ´ - 2/3X > - 4 ´ 3 =

- 2X > - 12

Then deal with the remaining whole numbers:

- 2X > - 12 =

- 2X ÷ 2 > - 12 ÷ 2 =

- X > - 6

Then, deal with the negative number:

- X > - 6 =

- X + 6 > - 6 + 6 =

- X + 6 > 0

Finally, isolate the unknown variable as a positive number:

- X + 6 > 0 =

- X + X + 6 > 0 + X =

6 > X =

X < 6

Example 3:

You will also be asked to divide polynomials. In order to solve this type of problem, you must to long division of the polynomial:

                x + 2

x - 3)x² - x + 6

         x² - 3x

        ______

                2x + 6

                2x + 6

                _____

                        0