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(x+3)(x+2)we need to multiply each term by both terms in the other bracketFOIL helps us remember the process. First, Outer, Inner, Last so we don't forget any of them.Fist - in this case multiply the firs...

The most important thing to remember when expanding brackets is to make sure that all terms in the one brackets have been multiplied with all the terms in the other.In this case we have two terms in each ...

Subsitute in u = 3x^2 + 6x and use chain rule to get dy/dx = dx/du x dy/dx to get dy/dx = 2(6x+6)e^(3x^2 +6)

a) We compare the expansion given to the standard binomial expansion (remembering the powers of k).(1+kx)ⁿ=1+n(kx)+(n(n-1)/2)(kx)²+...As this is true for all x (for which the expansi...

First, recall the Product rule: f(x)=g(x)*h(x), f'(x)=h(x)*g'(x)+h'(x)*g(x)This reveals the next step, to find the derivatives of our two subsidiary functions(g and h) d/dx * (sin4x) = 4cos(4x) , and d/dx...