1.

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

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Answer

To Do

  • To verify that x³ + y³ = (x + y) (x² - XY + y²)

Step By Step Explanation

In this we NEED to verify that x³ + y³ = (x + y) (x² - xy + y²)

Let's solve the L.H.S. and R.H.S. part of the EQUATION to verify. So let's do it !!

L. H. S. ⤵

\longmapsto\bf {\green{{x}^{3} + {y}^{3}}}

R. H. S. ⤵

\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}}}

x³ + y³ = x³ + y³

L.H.S. = R.H.S.

Hence, proved.

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