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| Factorisation |
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| If a polynomial can be written as the product of two or more expressions, then each expression is called the factor of the given polynomial. |
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| (i) Common factors |
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| (ii) By expressing as difference of squares |
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| (iii) By grouping |
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| (iv) Trinomials |
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| (v) Sum or difference of cubes |
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| Illustrations: |
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| Type (i) By taking out common factors from all the terms of a polynomial |
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| 8a3 b - 6a2b2 = 2a2b (4a - 3b) |
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| Type (ii) By expressing the polynomial as the difference of two squares |
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| 121x2 - 25y2 = (11x)2 - (5y)2 |
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| = (11x + 5y) (11x - 5y) [Using the identity a2-b2=(a-b)(a+b)] |
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| Factorise: (5a + 6b)2 - 49b2 |
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| Let x = 5a + 6b |
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| Then the given expression |
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| = (x)2 - (7b)2 |
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| = (x + 7b) (x - 7b) |
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| Re-substituting the value of x, we get |
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| = [(5a + 6b + 7b)] [(5a + 6b) - 7b] |
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| = (5a + 6b + 7b) (5a + 6b - 7b) |
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| = (5a + 13b) (5a - b) |
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