Question

3/1-a^3+3/1+a^3+6/1+a^6+12/1+a^12+24/1+a^24+48/1+a^48=?​

Answer 1

96+а^6+а^12+а^24+а^48=а^48+а^24+а^12+а^6+96

Answer 2

To solve the expression, let's try to simplify it step by step:

1. Combine the fractions with the same denominator: (3/1) + (3/1) + (6/1) + (12/1) + (24/1) + (48/1) = 3 + 3 + 6 + 12 + 24 + 48 = 96

2. Now, we need to factor the expression in the denominators of the fractions: 1 - a^3 = (1 - a^3) 1 + a^3 = (1 + a^3) 1 + a^6 = (1 + a^6) 1 + a^12 = (1 + a^12) 1 + a^24 = (1 + a^24) 1 + a^48 = (1 + a^48)

3. Notice that the denominators are in the form of a difference of cubes and sum of cubes. We can factor them further using those formulas: Difference of cubes: a^3 - b^3 = (a - b)(a^2 + ab + b^2) Sum of cubes: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

   Applying these formulas, we get: 1 - a^3 = (1 - a)(1 + a + a^2) 1 + a^3 = (1 + a)(1 - a + a^2) 1 + a^6 = (1 + a^3)(1 - a^3) = (1 + a)(1 - a + a^2)(1 - a)(1 + a + a^2) 1 + a^12 = (1 + a^6)(1 - a^6) = (1 + a)(1 - a + a^2)(1 - a)(1 + a + a^2)(1 + a^3)(1 - a^3) 1 + a^24 = (1 + a^12)(1 - a^12) = (1 + a)(1 - a + a^2)(1 - a)(1 + a + a^2)(1 + a^3)(1 - a^3)(1 + a^6)(1 - a^6) 1 + a^48 = (1 + a^24)(1 - a^24) = (1 + a)(1 - a + a^2)(1 - a)(1 + a + a^2)(1 + a^3)(1 - a^3)(1 + a^6)(1 - a^6)(1 + a^12)(1 - a^12)

4. Now, the expression becomes: 96 * (1 + a)(1 - a + a^2)(1 - a)(1 + a + a^2)(1 + a^3)(1 - a^3)(1 + a^6)(1 - a^6)(1 + a^12)(1 - a^12)

That's the simplified form of the expression. If you have specific values for 'a', you can further evaluate the expression numerically.