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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)

Answered by Roisin G. • Maths tutor

3340 Views

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, 2x⁴ will become (2x⁴⁺¹)/(4+1) = (2x⁵)/5, -4x<...

Answered by Rebecca M. • Maths tutor

7375 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 3x², to integrate a simple function of x li...

Answered by Jonathan O. • Maths tutor

8177 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!}x²+{[n(n-1)(n-2)]/3!}x

Answered by Sarah M. • Maths tutor

10959 Views

Why does differentiation give us the results that it does?

A quick analysis here is based on the fact that y=(x²). 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 cha...

Answered by Alexander A. • Maths tutor

4099 Views