2(a²+1/a²)-(a-1/a)-7

asked by guest
on Mar 21, 2025 at 8:28 pm



You asked:

Evaluate the expression: 2(a2+1a2)−(a−1a)−72 \left({a}^{2} + \frac{1}{{a}^{2}}\right) - \left(a - \frac{1}{a}\right) - 7

MathBot Answer:

Evaluated



2(a2+1a2)−(a−1a)−7=2a2−a−7+1a+2a2\displaystyle 2 \left({a}^{2} + \frac{1}{{a}^{2}}\right) - \left(a - \frac{1}{a}\right) - 7 = 2 a^{2} - a - 7 + \frac{1}{a} + \frac{2}{a^{2}}

Expanded

2(a2+1a2)−(a−1a)−7=2a2−a−7+1a+2a22 \left({a}^{2} + \frac{1}{{a}^{2}}\right) - \left(a - \frac{1}{a}\right) - 7 = 2 a^{2} - a - 7 + \frac{1}{a} + \frac{2}{a^{2}}

Factored

2(a2+1a2)−(a−1a)−7=(2a+1)(a−2)(a2+a−1)a22 \left({a}^{2} + \frac{1}{{a}^{2}}\right) - \left(a - \frac{1}{a}\right) - 7 = \frac{\left(2 a + 1\right) \left(a - 2\right) \left(a^{2} + a - 1\right)}{a^{2}}

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