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Expand (x+2)(x-3)(x+4)^2

(x+2)(x-3)(x+4)^2 = (x^2 - x - 6)(x^2 + 8x + 16) = (x^4 + 8x^3 +16x^2 - x^3 - 8x^2 -16x - 6x^2 - 48x - 96) = x^4 +7x^3 + 2x^2 - 64x - 96)
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Answered by Roisin G. • Maths tutor
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Find ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx

When integrating, you need to add one to the power and divide the term by the power. We will consider each term individually, 2x 4 will become (2x 4+1 )/(4+1) = (2x 5 )/5, -4x -0.5 will become (-4x -0.5+1 )/...
RM
Answered by Rebecca M. • Maths tutor
7462 Views

A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).

As f '(x) is the differential of f(x) we have to first integrate f '(x). To do this we take each term individually and integrate it. So starting with 3x 2 , to integrate a simple function of x like this we h...
JO
Answered by Jonathan O. • Maths tutor
8292 Views

how do you do binomial expansion when the power is a negative

There is a simple equation, similar to the normal binomial expansion, thats easy to remember once youve used it a few times. (1+x) n =1+nx+{[n(n-1)]/2!}x 2 +{[n(n-1)(n-2)]/3!}x 3 +... This looks complicated ...
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Answered by Sarah M. • Maths tutor
11128 Views

Why does differentiation give us the results that it does?

A quick analysis here is based on the fact that y=(x 2 ). A big change is worked out between two points. The gradient between x=1 and x=2 is equal to 3. BUT we know the gradient is constantly changing so thi...
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Answered by Alexander A. • Maths tutor
4211 Views