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Simplify \( (x+2y+z)^2-(x^2+4y^2+z^2) \).\( (x+2y+z)^2-(x^2+4y^2+z^2) \) को सरल कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(4xy+4yz+2xz\)\(4xy+4yz+2xz\)
First expand \((x+2y+z)^2\):
\[(x+2y+z)^2=x^2+(2y)^2+z^2+2\cdot x\cdot 2y+2\cdot x\cdot z+2\cdot 2y\cdot z\]
\[=x^2+4y^2+z^2+4xy+2xz+4yz\]
Now subtract \(x^2+4y^2+z^2\):
\[(x^2+4y^2+z^2+4xy+2xz+4yz)-(x^2+4y^2+z^2)=4xy+2xz+4yz\]
So the simplified form is \(4xy+4yz+2xz\) (same terms).पहले \((x+2y+z)^2\) का विस्तार कीजिए:
\[(x+2y+z)^2=x^2+(2y)^2+z^2+2\cdot x\cdot 2y+2\cdot x\cdot z+2\cdot 2y\cdot z\]
\[=x^2+4y^2+z^2+4xy+2xz+4yz\]
अब \(x^2+4y^2+z^2\) घटाइए:
\[(x^2+4y^2+z^2+4xy+2xz+4yz)-(x^2+4y^2+z^2)=4xy+2xz+4yz\]
इसलिए सरल रूप \(4xy+4yz+2xz\) है (यही पद हैं)।
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