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What is the product of (x+a) and (x+b)?

  • A.x²+ (a-b)x + ab
  • B.x² + (a+b)x - ab
  • C.x² + (a+b)x - ab
  • D.x² + (a+b)x + ab

Answer: D

Expand term by term.

\[ (x+a)(x+b) = x^{2} + bx + ax + ab \]

\[ = x^{2} + (a+b)x + ab \]

The coefficient of \( x \) is the sum of the two constants and the last term their product - the standard pattern used when factorising quadratics.

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