factor of 15(X2 +2xy)
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Step-by-step explanation: Start by factoring 15x2+2xy−24y2 and then hope for the best. Factor this by decomposition or by magic.
Note that 15×24=360 . So we seek two numbers with product being 360 and difference 2 with the larger assigned a positive sign. The numbers are 20 and 18 . So continue in the following way:
15x2+2xy−24y2=15x2+20xy−18xy−24y2=5x(3x+4y)−6y(3x+4y)=(5x−6y)((3x+4y).
Now for the hoping part. The −6 could mess the whole thing up. In fact, had it been some other number, the quadratic would not factor. Here’s what we do. Set y=0 and factor the result. The factored form is (5x+3)(3x−2) with the important numbers being 3 and −2 . This suggests that
15x2+2xy−24y2−x+24y−6=(5x−6y+3)(3x+4y−2) .
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