Mathematics
Factorise the following:
2x2 + 13xy - 24y2
Factorisation
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Answer
To factorise 2x2 + 13xy - 24y2, we want to find two real numbers whose sum is 13 and product is 2 × (-24) = -48. By trial, we see that 16 + (-3) = 13 and 16 × (-3) = -48.
∴ 2x2 + 13xy - 24y2 = 2x2 + 16xy + (-3xy) - 24y2
= 2x2 + 16xy - 3xy - 24y2
= 2x(x + 8y) - 3y(x + 8y)
= (x + 8y)(2x - 3y).
Hence, 2x2 + 13xy - 24y2 = (x + 8y)(2x - 3y).
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