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The point of using a substitution when dealing with integrals is to reduce the problem from a very complicated integral to a simplistic one. How can we achieve this with our integral? Well, we know that w...

The factor theorem states that if (x+a) is a factor of f(x), then f(-a)=0. This basically means that if (x+a) is a factor of f(x), then when (x+a)=0, f(x)=0, i.e. when x=-a, f(-a)=0. Our (x+a) in this cas...

The points where the lines cross are the points where the two equations equal each other. To do this we solve simultaneous equations. Call equations as follows:(a) 3x - y = 4(b) x² + 7y = 5 Fir...

P is currently the subject of the formula, y needs to be isolated. To do so first we need to get rid of the square root on the right side of the formula. Opposite to square root is square, so if we square...

To expand the brackets we consider each bracket separately, (2m-3) which is multiplied by (m+1). Consider first the first identity in each bracket:2m x m = 2m²Then consider the first identity a...