To solve bracket algebra, the key is to understand the distributive property, which states that everything inside the brackets must be multiplied by the term or number outside the bracket. Here's a breakdown of the process:
Understanding Bracket Algebra
Bracket algebra, also known as expanding brackets, involves simplifying expressions that include parentheses (brackets) by applying the distributive property. This property is fundamental to algebraic manipulations.
Steps to Solve Bracket Algebra
Here are the steps on how to solve bracket algebra expressions:
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Identify the Brackets: Locate all the bracketed terms in your algebraic expression.
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Distribute: The provided reference states, "make sure that everything inside the bracket is multiplied by the term (or number) outside the bracket". This is the core of solving bracket algebra. Multiply each term inside the brackets by the term outside the brackets.
- For example: If you have
a(b + c), you must multiply 'a' by both 'b' and 'c', resulting inab + ac. - Consider:
2(x + 3). Distribute the2across the terms inside the bracket:2 * x + 2 * 3, which simplifies to2x + 6.
- For example: If you have
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Simplify: After expanding the brackets, simplify the expression by combining like terms.
- For example: If you had
2x + 6 + 3x -1, combine like terms to get5x + 5.
- For example: If you had
Examples of Solving Bracket Algebra
| Expression | Step-by-step solution | Simplified Expression |
|---|---|---|
| 3(x + 2) | 3 x + 3 2 | 3x + 6 |
| 4(2y - 1) | 4 2y - 4 1 | 8y - 4 |
| -2(a + 5) | -2 a + (-2 5) | -2a - 10 |
| 5(x - 2) + 3(x + 1) | 5 x - 5 2 + 3 x + 3 1 | 5x - 10 + 3x + 3 |
| Combine like terms: 5x + 3x -10 + 3 | 8x - 7 |
Key Insights
- Sign Awareness: Be particularly careful when a negative sign precedes the brackets. It changes the sign of each term inside the bracket.
- Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) - Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction.
- Practice: Consistent practice helps in mastering bracket expansion and simplification.
By following these steps and understanding the distributive property, you can effectively solve a wide range of algebraic expressions involving brackets. Remember that expanding the brackets to produce an equivalent equation is the key to simplifying these expressions before final simplification.
