Completing-The-Square Edexcel Higher

Completing the square

How can I rewrite the first two terms of a quadratic expression as the difference of two squares?

• Look at the quadratic expression x² + bx + c 

• The first two terms can be written as the difference of two squares using the following rule

is the same as where is half of 

• Check this is true by expanding the right-hand side

  • Is the same as <img alt=”open parentheses x plus 1 close parentheses squared minus 1 squared” data-mathml='<math ><semantics><mrow><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><msup><mn>1</mn><mn>2</mn></msup></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ height=”23″ role=”math” 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