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Find the simplified form of \((a+b+c)^2-(a^2+b^2+c^2)\).\((a+b+c)^2-(a^2+b^2+c^2)\) का सरलीकृत रूप ज्ञात कीजिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(2(ab+bc+ca)\)\(2(ab+bc+ca)\)
First expand \((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\). Then subtract \((a^2+b^2+c^2)\):
\((a+b+c)^2-(a^2+b^2+c^2)=2ab+2bc+2ca=2(ab+bc+ca)\).पहले \((a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca\) को विस्तार करें। फिर \((a^2+b^2+c^2)\) घटाएँ:
\((a+b+c)^2-(a^2+b^2+c^2)=2ab+2bc+2ca=2(ab+bc+ca)\)।
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