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The trick here is to use a technique called the difference of squares. If we multiply the top and bottom of the fraction by the conjugate* of the denominator, we can remove any square root terms from the ...

First take natural logs of both sides, giving us: ln(3^x * e^4x) = ln(e⁷).  The RHS can be simplified using the definition of natural logs, so ln(e⁷) = 7.

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The at first can seem very challenging and you won't be able to tackle this question quickly using simple factorisation, which you can often do for many questions. It is best in this case then to use the ...

For the first part, use the 'complete the square method', which gives (x-7/2)² -49/4+2, simplified to (x-7/2)²-41/4. To find the answer for the second part, set x=7/2 so that the bra...

We know thst the binomial expansion formula is (1+x)ⁿ = 1+nx +(n)(n-1)(x²)/2! ...etc

Thus we want to rearrange the expression we are given into the form (1+x)ⁿ so t...