Factorise:
72x2−10x−427\sqrt{2}x^2 - 10x - 4\sqrt{2}72x2−10x−42.
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72x2−10x−42=72x2−14x+4x−42=72x(x−2)+4(x−2)=(x−2)(72x+4)7\sqrt{2}x^2 - 10x - 4\sqrt{2}\\[1em] = 7\sqrt{2}x^2 - 14x + 4x - 4\sqrt{2}\\[1em] = 7\sqrt{2}x(x - \sqrt{2}) + 4(x - \sqrt{2})\\[1em] = (x - \sqrt{2})(7\sqrt{2}x + 4)72x2−10x−42=72x2−14x+4x−42=72x(x−2)+4(x−2)=(x−2)(72x+4)
Hence, 72x2−10x−42=(x−2)(72x+4)7\sqrt{2}x^2 - 10x - 4\sqrt{2} = (x - \sqrt{2})(7\sqrt{2}x + 4)72x2−10x−42=(x−2)(72x+4).
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