Squaring brackets
Squaring Brackets
Introduction
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Squaring brackets refers to multiplying an bracketed term by itself.
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This process is crucial in algebraic computation and showcases the importance of order of operations and the distributive property.
Squaring Brackets Rule
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The expression inside the bracket is multiplied by itself. It’s not just squaring the individual terms inside the brackets - the bracketed quantity is treated as a whole.
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The process follows binomial expansion, resulting in the square of the first term, plus twice the product of the two terms, plus the square of the second term.
Step-by-Step Guide for Squaring Brackets
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Identify the term inside the bracket.
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Write the bracketed term twice as you’re multiplying it by itself.
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Use the FOIL method to multiply out the brackets (First, Outer, Inner, Last terms).
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Carefully pay attention to the signs of terms in brackets during the multiplication process.
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Combine like terms (if any).
Examples
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For the equation (x + 3)², The operation will be (x + 3)(x + 3). Applying the FOIL method, you get x² + 3x + 3x + 9, which simplifies to x² + 6x + 9.
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For the equation (y - 4)², The operation will be (y - 4)(y - 4). Using the FOIL method, it turns into y² - 4y - 4y +16, which simplifies to y² - 8y + 16.
Conclusion
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Squaring brackets is essential as it serves as the basis for the development of higher-level algebraic calculations.
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Regular practice is crucial to understand this concept fully and to ensure you remember to apply the FOIL method accurately. Careful attention to signs can help avoid common errors!