# Past Papers’ Solutions | Edexcel | AS & A level | Mathematics | Core Mathematics 1 (C1-6663/01) | Year 2010 | January | Q#2

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**Question**

**a. **Expand and simplify

**b. **Express in the form , where a and b are integers.

**Solution**

**a. **

We are given;

Since ;

**b. **

We are given;

If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below.

ü If the denominator is of the form then multiply both numerator and denominator by .

ü If the denominator is of the form then multiply both numerator and denominator by .

ü If the denominator is of the form then multiply both numerator and denominator by .

From (a) we know that;

We can expand and simplify the denominator as follows.

We have algebraic formula;

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