MCQ
Factorize Completely $x^4 - 625$
- ✓$(x \div 5) (x - 5) (x^2 \div 25)$
- B$(x^2 - 25) (x^2 \div 5)$
- C$(x \div 5)^2 (x - 5)$
- D$(x \div 5) (x - 5)^2$
✓
Answer
Correct option: A.
$(x \div 5) (x - 5) (x^2 \div 25)$
A. $(x \div 5) (x - 5) (x^2 \div 25)$
Solution:
$x^4 - 625 = (x^2)^2 - (25)^2$
Apply the identity, $a^2 - b^2 = (a + b) (a - b)$
$\Rightarrow (x^2 + 25) (x^2 - 25)$
Factorize $(x^2 - 25)$ using the same identity.
$\Rightarrow (x^2 + 25) (x)^2 - (5)^2$
$\Rightarrow (x^2 + 25) (x + 5) (x - 5)$
Solution:
$x^4 - 625 = (x^2)^2 - (25)^2$
Apply the identity, $a^2 - b^2 = (a + b) (a - b)$
$\Rightarrow (x^2 + 25) (x^2 - 25)$
Factorize $(x^2 - 25)$ using the same identity.
$\Rightarrow (x^2 + 25) (x)^2 - (5)^2$
$\Rightarrow (x^2 + 25) (x + 5) (x - 5)$
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