1.

Verify x³ + y³ = (X + y) (x² -xy + y²)​

Answer» <html><body><h3><u>Answer</u></h3><p></p><h3><u>To </u><u>Do</u></h3><p></p><ul><li>To verify that x³ + y³ = (x + y) (x² - <a href="https://interviewquestions.tuteehub.com/tag/xy-747762" style="font-weight:bold;" target="_blank" title="Click to know more about XY">XY</a> + y²)</li></ul><p></p><h3><u>Step </u><u>By </u><u>Step </u><u>Explanation</u></h3><p></p><p>In this we <a href="https://interviewquestions.tuteehub.com/tag/need-25476" style="font-weight:bold;" target="_blank" title="Click to know more about NEED">NEED</a> to verify that x³ + y³ = (x + y) (x² - xy + y²)</p><p>Let's solve the L.<a href="https://interviewquestions.tuteehub.com/tag/h-1014193" style="font-weight:bold;" target="_blank" title="Click to know more about H">H</a>.S. and R.H.S. part of the <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> to verify. So let's do it !!</p><p></p><p><strong>L. </strong><strong>H. </strong><strong>S. </strong><strong> </strong><strong>⤵</strong></p><p><img align="absmiddle" alt="\longmapsto\bf {\green{{x}^{3} + {y}^{3}}}" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%5Clongmapsto%5Cbf%20%20%7B%5Cgreen%7B%7Bx%7D%5E%7B3%7D%20%20%2B%20%20%7By%7D%5E%7B3%7D%7D%7D" title="\longmapsto\bf {\green{{x}^{3} + {y}^{3}}}"/></p><p></p><p><strong>R. </strong><strong>H. </strong><strong>S. </strong><strong>⤵</strong></p><p><img align="absmiddle" alt="\longmapsto\tt (x + y)( {x}^{2} + {y}^{2} - xy) \\ \\\longmapsto\tt x( {x}^{2} + {y}^{2} - xy) + y( {x}^{2} + {y}^{2} - xy) \\ \\\longmapsto\tt {x}^{3} + \cancel{x{y}^{2}} \cancel{ - {x}^{2}y}+ \cancel {{x}^{2}y} + {y}^{3} \cancel{ - x {y}^{2}} \\ \\\longmapsto\bf {\pink{{x}^{3} + {y}^{3}}}" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%5Clongmapsto%5Ctt%20%28x%20%2B%20y%29%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%20xy%29%20%5C%5C%20%20%5C%5C%5Clongmapsto%5Ctt%20x%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%20xy%29%20%2B%20y%28%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%20xy%29%20%5C%5C%20%20%5C%5C%5Clongmapsto%5Ctt%20%7Bx%7D%5E%7B3%7D%20%2B%20%20%5Ccancel%7Bx%7By%7D%5E%7B2%7D%7D%20%20%5Ccancel%7B%20-%20%20%7Bx%7D%5E%7B2%7Dy%7D%2B%20%20%5Ccancel%20%7B%7Bx%7D%5E%7B2%7Dy%7D%20%2B%20%20%7By%7D%5E%7B3%7D%20%20%20%5Ccancel%7B%20-%20x%20%7By%7D%5E%7B2%7D%7D%20%5C%5C%20%20%5C%5C%5Clongmapsto%5Cbf%20%7B%5Cpink%7B%7Bx%7D%5E%7B3%7D%20%20%2B%20%20%7By%7D%5E%7B3%7D%7D%7D%20" title="\longmapsto\tt (x + y)( {x}^{2} + {y}^{2} - xy) \\ \\\longmapsto\tt x( {x}^{2} + {y}^{2} - xy) + y( {x}^{2} + {y}^{2} - xy) \\ \\\longmapsto\tt {x}^{3} + \cancel{x{y}^{2}} \cancel{ - {x}^{2}y}+ \cancel {{x}^{2}y} + {y}^{3} \cancel{ - x {y}^{2}} \\ \\\longmapsto\bf {\pink{{x}^{3} + {y}^{3}}}"/></p><p></p><p><strong>x</strong>³ + <strong>y</strong>³ = <strong>x</strong>³ + <strong>y</strong>³</p><p>L.H.S. = R.H.S.</p><p></p><p><strong><u>Hence</u></strong><strong><u>, </u></strong><strong><u>proved</u></strong><strong><u>.</u></strong></p><h2><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong><strong><u>_</u></strong></h2></body></html>


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