Mathematics
Factorise the following:
5x2 + 17xy - 12y2
Factorisation
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Answer
To factorise 5x2 + 17xy - 12y2, we want to find two real numbers whose sum is 17 and product is 5 × (-12) = -60. By trial, we see that 20 + (-3) = 17 and 20 × (-3) = -60.
∴ 5x2 + 17xy - 12y2 = 5x2 + 20xy - 3xy - 12y2
= 5x(x + 4y) - 3y(x + 4y)
= (x + 4y)(5x - 3y).
Hence, 5x2 + 17xy - 12y2 = (x + 4y)(5x - 3y).
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