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It's a simple arithmetic calculation. A is exactly b more than B means A = B + b So in this case What is 2500 more than 7000, it means what is 2500 + 7000 = 9500.
If a and b are rational, with a < b, then a + (b-a) [sqrt(2)/ 2] is an irrational number between a and b. This number is between a and b because sqrt(2)/2 is less than one and positive, so that a < a + (b-a) [sqrt(2)/3] < a + (b-a) [1] = b. To prove that a + (b-a) [sqrt(2)/2] is not rational, suppose that a + (b-a) [sqrt(2)/2] = p/q where p and q are integers. Then, sqrt(2) = ( p/q -a ) 2/(b-a) which is rational since the rationals are a field, closed under arithmetical operation, but sqrt(2) not rational (Look up the elementary proof if you do not know it.)
To factor a^4 - b^4 completely, you can use the formula for the difference of squares, which states that a^2 - b^2 = (a + b)(a - b). In this case, a^4 - b^4 is a difference of squares twice: (a^2)^2 - (b^2)^2. So, you can factor it as (a^2 + b^2)(a^2 - b^2). Then, factor a^2 - b^2 further using the difference of squares formula to get (a^2 + b^2)(a + b)(a - b), which is the complete factorization of a^4 - b^4.
2, i think
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