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Factorise fully the following: 12x^3 + 3x^2 + 15x

To factorise an equation entirely it is necessary to think of the commonality between all terms. In this case, not only 'x' is common in all the parts of the equation, but also '3'. Knowing this information ...
HB
Answered by Helena B. • Maths tutor
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A metal Sphere of radius Ym is melted down and remade into a cylinder of the same volume with height Ym with circular ends of radius 3m, find Y

The sphere has radius Y, so the volume of the sphere is 4/3 (pi) Y 3 , The volume is the same for the cyclinder so we know the volume of the cylinder in terms of Y. Cyclinder volume = area of circle face x h...
JC
Answered by James C. • Maths tutor
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What is Pythagoras's theorem?

Pythagoras's theorem is used to calculate the lengths of the sides of right-angled triangles. The theorem can be used to find the length of the third side of a right-angled triangle, as long as the lengths o...
SJ
Answered by Samuel J. • Maths tutor
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How would I differentiate a function such as f(x)=x^3(e^(2x))?

Here, f(x)=x 3 e 2x is a function consisting of two functions multiplied together, so we need to use the product rule. The product rule is as follows: where f(x)=u(x)v(x), f'(x)=u(x)v'(x)+u'(x)v(x). The firs...
LB
Answered by Lauren B. • Maths tutor
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Please Simplify: (2x^2+3x/(2x+3)(x-2))-(6/x^2-x-2))

Factorise both parts of the question. Our left side would become x(2x+3)/(2x+3)(x-2) and our right side would become 6/(x+1)(x-2). On our LHS the (2x+3) would cancel leaving x/x-2. In order to merge the frac...
OG
Answered by Omar G. • Maths tutor
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