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How do I do binomial expansions for positive integer n?

The general method for (a+b)^n is: 1)write out pascals triangle (see whiteboard) and stop at the nth row. Write this on a line. 2)write down the powers of a in ascending order (and simplify) 3)write down the...
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Answered by Daniel R. • Maths tutor
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How do I work out what integration method I should use to solve an integral?

A-Level Mathematics is about a wide range of topics, among which Integrating is key! While differentiation is a technique, whereby a set of rules can be used to approach problems, integration is an art, for ...
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Answered by Luigi C. • Maths tutor
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Show that x^2 - x +2 is positive for all values of x

(x-1/2) 2 = (x-1/2)(x-1/2)=x 2 -x+1/4, add 7/4 to get x 2 -x+2 therefore x 2 -x+2 = (x-1/2) 2 + 7/4 squared numbers always positive so (x-1/2) 2 >= 0 therefore (x-1/2) 2 + 7/4 is always positive
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Answered by Pearse M. • Maths tutor
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Vectors a and b are defined by a = 2i + 3j and b = 4i - 2j, find 3a-b in terms of i and j

3a = 6i + 9j -b = -4i + 2j 3a-b = (6i-4i) + (9j+2j) = 2i + 11j
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Answered by Pearse M. • Maths tutor
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Find ∫(4x - 2/(x^3)) dx

Using the integer rule 1/ (x n ) = x -n question becomes ∫(4x - 2(x -3 )) dx Then using the formula ∫x n dx = (x n+1 )/n+1 and assuming there may be an integer value (+c) the answer is 2(x 2 ) + x -2 + c
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Answered by Pearse M. • Maths tutor
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