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There are two ways to prove they intercept (you can choose whichever one you prefer). Say we have two straight lines, for example: r₁ = 3i + 4...

6x + 2y = 2 and 12x -3y =18 

Start by multiplying the first equation by two in order to balance both equations to have equal numbers of x

12x + 4y = 4 and 12x - 3y = 18

Rearrange both...

Here we have a product of two functions - they are being multiplied together - so we need to use the product rule. The product rule is: if y = u·v, dy/dx = v·u' + u·v' (where f' stands for df/dx). u = x^4...

Firstly we must take the 2 out of the bracket, as a binomial expansion must have a coefficent of 1

(2 + x) ⁵  = 2⁵ (1 + 0.5x) ⁵

Then, it is a good idea to qu...

'Simplest surd form' is a clue that quadratic factorising will not work for this question, so we must instead use the quadratic formula. It is always a good idea to quote this as marks are often available...