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Expanding and Factorising
Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.
Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.
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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)
Summary
For (x + 3)(x + 5) you get four products: x², 5x, 3x and 15. The two middle terms add to 8x, giving x² + 8x + 15. The grid (area) model shows the same four pieces as boxes.
First = the two front terms, Outer = the two ends, Inner = the two middle terms, Last = the two back terms. Carry every minus sign as part of its term to avoid the most common error.
For x² + 7x + 12 you need numbers that add to 7 and multiply to 12: that is 3 and 4, so it factorises to (x + 3)(x + 4). Always re-expand to check.
If you see a² − b² write it straight away as (a + b)(a − b) - the middle terms cancel. (a + b)² expands to a² + 2ab + b², not a² + b²: the 2ab middle term is the part people forget.
Hard words & meanings
| expand | to multiply out brackets so the expression has no brackets left |
| factorise | to write an expression as a product of brackets (factors) |
| binomial | an expression with exactly two terms, such as x + 3 |
| trinomial | an expression with three terms, such as x² + 7x + 12 |
| coefficient | the number multiplying a variable, e.g. 7 in 7x |
| like terms | terms with the same variable part that can be added, e.g. 5x and 3x |
| difference of two squares | an expression of the form a² − b², which factorises to (a + b)(a − b) |
| quadratic | an expression whose highest power of the variable is 2 |
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