MCQ
The value of $(\sqrt{\text{x}}+\sqrt{\text{y}})(\sqrt{\text{x}}-\sqrt{\text{y}})(\text{x}+\text{y})(\text{x}^2+\text{y}^2)$ is:
- A$(\text{x}^4+\text{y}^4)$
- ✓$(\text{x}^4-\text{y}^4)$
- C$(\text{x}+\text{y})^4$
- D$(\text{x}-\text{y})^4$
✓
Answer
Correct option: B.
$(\text{x}^4-\text{y}^4)$
$(\sqrt{\text{x}}+\sqrt{\text{y}})(\sqrt{\text{x}}-\sqrt{\text{y}})(\text{x}+\text{y})(\text{x}^2+\text{y}^2)$
$[(\sqrt{\text{x}})^2-(\sqrt{\text{y}})^2](\text{x}+\text{y})(\text{x}^2+\text{y}^2)$
$=(\text{x}-\text{y})(\text{x}+\text{y})(\text{x}^2+\text{y}^2)$
$=[(\text{x})^2-(\text{y})^2](\text{x}^2+\text{y}^2)$
$=(\text{x}^2-\text{y}^2)(\text{x}^2+\text{y}^2)$
$=(\text{x}^2)^2-(\text{y}^2)^2$
$=\text{x}^2-\text{y}^2$
$[(\sqrt{\text{x}})^2-(\sqrt{\text{y}})^2](\text{x}+\text{y})(\text{x}^2+\text{y}^2)$
$=(\text{x}-\text{y})(\text{x}+\text{y})(\text{x}^2+\text{y}^2)$
$=[(\text{x})^2-(\text{y})^2](\text{x}^2+\text{y}^2)$
$=(\text{x}^2-\text{y}^2)(\text{x}^2+\text{y}^2)$
$=(\text{x}^2)^2-(\text{y}^2)^2$
$=\text{x}^2-\text{y}^2$
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