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Using FOIL to expand the brackets we get

9 - 6root5 + 12root5 + 8*root5^2

Square rooting then squaring a number cancels out, so we are left with 8*5 or 40 for the last term.

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AB² = (1 - 7)² + (6 + 2)² = 36 + 64 = 100 If AB² = 100 then AB = 10

3x²+11x-4=0 #Factorise to find where the curve crosses the x axis (3x-1)(x+4)=0 #Each bracket equals 0 x=1/3, -4  #Integrate the curve between these two points to find the area enclosed in the ...

(x - 5) / (x² + 2x - 15) 

Let k(x) = f(x)g(x) then k'(x) = limit as h --> 0 of: (h(x+h)-h(x))/h = lim (f(x+h)g(x+h) - f(x)g(x))/h

We can factorise the numerator as:
f(x+h)g(x+h) - f(x)g(x) =f(x+h)g(x+h) -g(x)...