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Expand and simplify $ ( \\sqrt{7} + 2) \\cdot (\\sqrt{7} - 2) .$ - Edexcel - A-Level Maths Pure - Question 5 - 2009 - Paper 1

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Expand-and-simplify---$---(--\\sqrt{7}-+-2)--\\cdot-(\\sqrt{7}---2)-.$-Edexcel-A-Level Maths Pure-Question 5-2009-Paper 1.png

Expand and simplify $ ( \\sqrt{7} + 2) \\cdot (\\sqrt{7} - 2) .$

Worked Solution & Example Answer:Expand and simplify $ ( \\sqrt{7} + 2) \\cdot (\\sqrt{7} - 2) .$ - Edexcel - A-Level Maths Pure - Question 5 - 2009 - Paper 1

Step 1

Expand the expression

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Answer

To expand the expression, we can use the distributive property (also known as the FOIL method for binomials):

(7+2)(7−2)=7⋅7+7⋅(−2)+2⋅7+2⋅(−2)(\sqrt{7} + 2)(\sqrt{7} - 2) = \sqrt{7} \cdot \sqrt{7} + \sqrt{7} \cdot (-2) + 2 \cdot \sqrt{7} + 2 \cdot (-2)

Calculating each term:

  1. (\sqrt{7} \cdot \sqrt{7} = 7)
  2. (\sqrt{7} \cdot (-2) = -2\sqrt{7})
  3. (2 \cdot \sqrt{7} = 2\sqrt{7})
  4. (2 \cdot (-2) = -4)

Now, substituting these back in:

7−27+27−47 - 2\sqrt{7} + 2\sqrt{7} - 4

Step 2

Combine like terms

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Answer

Combining the like terms:

7−4+(−27+27)=3+0=37 - 4 + (-2\sqrt{7} + 2\sqrt{7}) = 3 + 0 = 3

Thus, the simplified expression is:

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