username5186778
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I understand how to do equations where the coefficient of x^2 is not 1, as well as normal quadratic equations. I do not know how to factorise equations where the number on the end is also squared. An explanation would be appreciated.
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jemima0103
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Factor 2x2+13xy+15y2
2x2+13xy+15y2
=(2x+3y)(x+5y)
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Sinnoh
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The factorised identity would just be in the form (ax + by)(cx + dy), so I think you can just use the standard method
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Legomenon
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The most important thing to note here is that it can still be viewed as a quadratic in x, i.e. something like ax^2+bx+c if you view y as a constant.

So factorising as you usually do for single-variable quadratics, you would want something like (2x+p)(x+q) where p and q multiply to give 15y^2 (with the cross term as well). As noted above, you will find that the natural choices p=5y and q=3y work. But the lesson to take away here is to always try to relate new problems to ones you already know how to solve.
Last edited by Legomenon; 1 year ago
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