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Building Mathematical Recipes
Building Mathematical Recipes
Imagine you're a chef with two types of recipes: one that combines simple ingredients into complex dishes (expanding), and another that breaks down complex dishes into their simple ingredients (factorising). In mathematics, these are reverse processes that help us work with quadratic expressions.
When we expand (x + 3)(x + 5), we're combining two simple brackets into a more complex expression: x² + 8x + 15. When we factorise x² + 8x + 15, we're breaking it back down into its "ingredients": (x + 3)(x + 5). Both skills are essential for solving quadratic equations and understanding how algebraic expressions behave.
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Common Mistakes to Avoid
- Sign errors: (x - 3)(x + 2) ≠ x² + x - 6
Correct: x² - x - 6 (careful with the middle term!) - Forgetting the x² term: Always check your first term is x²
- Wrong factor pairs: For x² + 7x + 10, don't use (x + 1)(x + 10)
Check: 1 + 10 = 11 ≠ 7 - Perfect square confusion: (x + 3)² ≠ x² + 9
Correct: (x + 3)² = x² + 6x + 9 - Missing negative signs: When one factor is negative, be extra careful with signs throughout
Now try it yourself
Quiz · Question 1 of 12
Expand (x + 5)².
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