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Factorise 100-x^2

Via inspection, one can factorise this via the difference of squares; since a^2-b^2 = (a+b)(a-b), therefore:100-x^2 = (10-x)(10+x)
HM
Answered by Howard M. • Maths tutor
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Via the product rule, or otherwise, differentiate 'y = xsin(x)'.

SInce, for y = uv, dy/dx = uv' + vu', where u' = du/dx, therefore:dy/dx = (1 sin(x)) + (x cos(x)) = sin(x) + xcos(x)
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Answered by Howard M. • Maths tutor
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Solve the simultaneous equations: 3y + 2x = 10, 4x - y + 3 = 2

The first step whenever you are given an equation is to group like terms. By this I mean put all the terms with the same letter next to it together and, in this case, the numbers without a letter. For the eq...
TM
Answered by Tom M. • Maths tutor
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What is the area enclosed by the functions x^2 and sqrt(x)?

First, let's see how the plot of the functions looks like (draw on whiteboard). Next, let's calculate where the functions intersect by setting x 2 = sqrt(x) and solving for x (manipulate by squaring both sid...
Answered by • Maths tutor
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v^2=u^2 + 2as u=12 a=-3 s = 18 Find v

First we can plug in the values we already know into the equation we would get: V 2 = 12 2 + (2 x -3 x 18) then we would seperate the two multiplications on the right hand side12 x 12 = 144 2 x -3 x 18 = -6 ...
OB
Answered by Oscar B. • Maths tutor
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