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Factorization Of Algebraic Expressions — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions1 Mark
MCQ
The expression $x^4+4$ can be factorized as:
  • ✓
    $\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
     
  • B
     $\left(x^2+2 x+2\right)\left(x^2+2 x-2\right)$
     
  • C
    $\left(x^2-2 x-2\right)\left(x^2-2 x+2\right)$
     
  • D
    $\left(x^2+2\right)\left(x^2-2\right)$
✓

Answer

Correct option: A.
$\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$
 
$x^4+4$
$=x^4+4+4 x^2-4 x^2$
$=\left(x^4+4 x^2+4\right)-4 x^2$
$=\left(x^2+2\right)^2-(2 x)^2$
$=\left(x^2+2-2 x\right)\left(x^2+2+2 x\right)$
$=\left(x^2+2 x+2\right)\left(x^2-2 x+2\right)$

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