Expand:
(2a−1a)2\Big(2a -\dfrac{1}{a}\Big)^2(2a−a1)2
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Using the formula:
(∵ (x + y)2 = x2 + 2xy + y2)
=(2a)2−2×2a×1a+(1a)2=4a2−4aa+1a2=4a2−4+1a2= (2a)^2 - 2 \times 2a \times \dfrac{1}{a} + \Big(\dfrac{1}{a}\Big)^2\\[1em] = 4a^2 - \dfrac{4a}{a} + \dfrac{1}{a^2}\\[1em] = 4a^2 - 4 + \dfrac{1}{a^2}=(2a)2−2×2a×a1+(a1)2=4a2−a4a+a21=4a2−4+a21
Hence, (2a−1a)2\Big(2a -\dfrac{1}{a}\Big)^2(2a−a1)2 = 4a2−4+(1a2)4a^2 - 4 + \Big(\dfrac{1}{a^2}\Big)4a2−4+(a21)
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Evaluate:
(a + bc) (a - bc) (a2 + b2c2)
(a+12a)2\Big(a +\dfrac{1}{2a}\Big)^2(a+2a1)2
(a + b - c)2
(a - b + c)2
