Factorise :
23x2+x−532\sqrt{3}x^2 + x - 5\sqrt{3}23x2+x−53
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Given,
=23x2+x−53=23x2+6x−5x−53=23x(x+3)−5(x+3)=(x+3)(23x−5).\phantom{=} 2\sqrt{3}x^2 + x - 5\sqrt{3} \\[1em] = 2\sqrt{3}x^2 + 6x - 5x - 5\sqrt{3} \\[1em] = 2\sqrt{3}x(x + \sqrt{3}) - 5(x + \sqrt{3}) \\[1em] = (x + \sqrt{3})(2\sqrt{3}x - 5).=23x2+x−53=23x2+6x−5x−53=23x(x+3)−5(x+3)=(x+3)(23x−5).
Hence, 23x2+x−53=(x+3)(23x−5).2\sqrt{3}x^2 + x - 5\sqrt{3} = (x + \sqrt{3})(2\sqrt{3}x - 5).23x2+x−53=(x+3)(23x−5).
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Evaluate :
5.67×5.67×5.67+4.33×4.33×4.335.67×5.67−5.67×4.33+4.33×4.33\dfrac{5.67 \times 5.67 \times 5.67 + 4.33 \times 4.33 \times 4.33}{5.67 \times 5.67 - 5.67 \times 4.33 + 4.33 \times 4.33}5.67×5.67−5.67×4.33+4.33×4.335.67×5.67×5.67+4.33×4.33×4.33
9x2 + 3x - 8y - 64y2
14(a+b)2−916(2a−b)2\dfrac{1}{4}(a + b)^2 - \dfrac{9}{16}(2a - b)^241(a+b)2−169(2a−b)2
2(ab + cd) - a2 - b2 + c2 + d2
