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Simplify $(3 + \sqrt{5})(3 - \sqrt{5})$. - Edexcel - A-Level Maths Pure - Question 3 - 2007 - Paper 1

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Simplify-$(3-+-\sqrt{5})(3---\sqrt{5})$.---Edexcel-A-Level Maths Pure-Question 3-2007-Paper 1.png

Simplify $(3 + \sqrt{5})(3 - \sqrt{5})$.

Worked Solution & Example Answer:Simplify $(3 + \sqrt{5})(3 - \sqrt{5})$. - Edexcel - A-Level Maths Pure - Question 3 - 2007 - Paper 1

Step 1

Expand the expression

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Answer

To simplify the expression, we can use the formula for the difference of squares, which is given by:

a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)

In our case:

  • Let a=3a = 3
  • Let b=5b = \sqrt{5}

Thus, we have:

(3+5)(3−5)=32−(5)2(3 + \sqrt{5})(3 - \sqrt{5}) = 3^2 - (\sqrt{5})^2

Step 2

Calculate the squares

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Answer

Now, let's compute the squares:

  • 32=93^2 = 9
  • (5)2=5(\sqrt{5})^2 = 5

Substituting these values into the expression, we have:

9−59 - 5

Step 3

Simplify the result

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Answer

Finally, simplifying gives:

9−5=49 - 5 = 4

Thus, the simplified result of the expression is 44.

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