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First we must multiply out the brackets, using FOIL (first, outer, inner, last). This gives f(x) = -x^3 + 5x^2 - 3x + 15. Alternatively you could leave the brackets as they are, and use the product rule to d...

Quarks are the building blocks of protons and neutrons, as found in the nucleus of atoms. They are as far as we know, fundamental particles, but this could change in the future. There are 6 types, named up, ...

Differentiation is a very important tool for mathematicians. Although finding the gradient of a line can seem to lack a point, it does have some very important applications. For example, in mechanics the vel...

On the 16th of August 2004, Boscastle, a small fishing village on the North coast of Cornwall, experienced one of the worst flash floods Britain has ever seen, 1 in 400 year flood. Two and a half miles up st...

y = cos2θ . 2) cos2θ = 1 - 2sin²θ. 3) x = 2sinθ. 4) x² = 4sin²θ. 5) (1/2)x² = 2sin²θ. 6) y = 1 - (1/2)x².