Topic Content:
- Expressions with Brackets
In AlgebraAlgebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them. More, letters stand for numbers. The number can be whole, positive or negative. To solve algebraic expressions containing brackets, we solve the brackets first e.g.
a. \( \scriptsize 5x \: + \: (4x \: – \: 3x) \)
The bracket contains the expression 4x – 3x which is equal to x
4x – 3x = x
We can then solve the whole equation since we have solved what was in the brackets
∴ \( \scriptsize 5x \: + \: (4x \: – \: 3x) \\ \scriptsize = 5x \: + \: x \\ = \scriptsize 6x \)
b. \( \scriptsize 9x \: – \: (5x \: + \: 2x)\)
The bracket contains the expression 5x + 2x which is equal to 7x
5x + 2x = 7x
We can then solve the whole equation since we have solved what was in the brackets
∴ \( \scriptsize 9x \: – \: (5x \: + \: 2x) \\ \scriptsize 9x \: – \: 7x \\ = \scriptsize 2x \)
Rules for Removing Brackets in Algebraic:
Remember:
\( \scriptsize + \: \times \: – \: = \: \: – \) (plus times minus = minus)
\( \scriptsize – \: \times \: + \: = \: \: – \) (minus times plus = minus)
\( \scriptsize – \: \times \: – \: = \: \: + \) (minus times minus = plus)
\( \scriptsize + \: \times \: + \: = \: \: + \) (plus times plus = plus)
(i) “+ sign“ before a bracket multiplies everything within the bracket and hence does not change the sign of terms in the bracket e.g.
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