Expanding two or more brackets
Expanding Two or More Brackets
Introduction
- The process of expanding two or more brackets is a fundamental concept in algebra.
- This procedure is also known as FOIL (First Outer Inner Last), which represents the order in which the terms should be multiplied.
The Expand Rule
- In order to expand two brackets, each term in the first bracket is multiplied by each term in the second bracket.
- The acronym FOIL reminds you to multiply the First terms in each bracket, the Outer terms, the Inner terms, and finally the Last terms in each bracket.
- Ensure the correct handling of positive and negative numbers.
Step-by-Step Guide for Expanding Two or More Brackets
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Identify the terms in the first and second brackets.
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Begin by multiplying the first term in the first bracket with the first term in the second bracket.
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Then multiply the outer terms (first term in the first bracket and the last term in the second bracket).
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Next up, multiply the inner terms (last term in the first bracket and first term in the second bracket).
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Finally, multiply the last terms in the first and second bracket.
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Combine your results, ensuring that you have managed each term’s sign correctly.
Examples
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In the expression (x - 2)(x + 3), you multiply ‘x’ and ‘x’ to get x^2, then ‘x’ and ‘3’ to get 3x, then ‘-2’ and ‘x’ to get -2x, finally ‘-2’ and ‘3’ to get -6. This results in the expansion x^2 + x - 6.
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With the equation (a + 4)(a - 4), ‘a’ and ‘a’ multiply to give a^2, ‘a’ and ‘-4’ multiply to give -4a, ‘4’ and ‘a’ multiply to give 4a, and ‘4’ and ‘-4’ multiply to give -16. This results in the expansion a^2 - 16, bearing in mind that the 4a and -4a cancel out.
Conclusion
- The ability to expand two or more brackets is a critical foundation for tackling complex algebraic equations.
- Practice with an assortment of equations and pay close attention to managing positive and negative terms.