#### Simplifying Algebraic Expressions

- a² is short for a × a.
- When simplifying arithmetic or algebraic expressions, the
*order of operations*is important.- If there are no brackets, do multiplication or division before addition and subtraction.
- If there are brackets, first simplify the terms inside them.

- When removing brackets:
- A positive sign outside the bracket (on the left hand side)
*does not*change the sign of each term inside the bracket. For example:- 2 + (x + 2) = 2 + x + 2 = x + 4
- 3x + (2y – 4) = 3x + 2y – 4

- A negative sign outside the bracket (on the left hand side)
*does*change the sign of each term inside the bracket. For example:- 2 – (x + 2) = 2 – x – 2 = -x
- 3x – (2y – 4) = 3x – 2y + 4

- A positive sign outside the bracket (on the left hand side)

__Examples__

__Examples__

- 2a × 3
- = 2 × a × 3
- = 2 × 3 × a
- = 6 × a
- = 6a

- 6b × 4b
- = 6 × b × 4 × b
- = 6 × 4 × b × b
- = 24 × b²
- = 24b²

- 8ab × 7a
- = 8 × a × b × 7 × a
- = 8 × 7 × a × a × b
- = 56 × a² × b
- = 56a²b

^{14a}/_{7}- =
^{14 × a}/_{7} - =
^{7 × 2a}/_{7} - =
^{1 × 2a}/_{1} - = 2a

- =
^{1}/_{3}of 36c- =
^{36 × c}/_{3} - =
^{3 × 12c}/_{3} - =
^{1 × 12c}/_{1} - = 12c

- =
- 24d²e ÷ 3de
- =
^{24 × d² × e}/_{3 × d × e} - =
^{3 × 8 × d × d × e}/_{3 × d × e} - =
^{1 × 8 × 1 × d × 1}/_{1 × 1 × 1} - = 8d

- =
- Find the value of 16 × 2 – 3 + 14 ÷ 7.
- = (16 × 2) – 3 + (14 ÷ 7)
- = 32 – 3 + 2
- = 32 + 2 – 3
- = 34 – 3
- = 31

- Simplify 7 × 3a – (3a + 5a) × 2.
- = 7 × 3a – 8a × 2
- = (7 × 3a) – (8a × 2)
- = 21a – 16a
- = 5a

- Simplify (6x – 5y) + (3y + 4x)
- = 6x – 5y + 3y + 4x
- = 6x + 4x + 3y – 5y
- = 10x – 2y
: There is no sign before the first bracket; we take it to be positive.__NOTE__

- (6x – y) – (7x – 2y)
- = 6x – y – 7x + 2y
- = 6x – 7x + 2y – y
- = -x + y
**or**y – x

- The greater of two consecutive numbers is x. (
**NOTE**: Two whole numbers are consecutive when their difference is 1. For example, 5 and 6 are consecutive numbers; 49 and 50 are also consecutive. In algebra, x and x + 1 or y – 1 and y are consecutive, provided x and y are whole numbers)- Find the sum of the two numbers.
- If x is the greater of the two numbers, the lower number is x – 1.
- ∴ The sum of the two numbers = x + (x – 1)
- = x + x – 1
- ∴ The sum of the two numbers = 2x – 1

- Subtract the sum of the two numbers from 5x.
- = 5x – (2x – 1)
- = 5x – 2x + 1
- = 3x + 1

- Find the sum of the two numbers.