Question

Verify : (ii) x³ - y³ = (x-y)(x² + xy + y²)

Answer 1

HEYA!!!!.
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➡️x3-y3 = (x-y)(x2+xy+y2)
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R.H.S
(x-y)(x2+xy+y2)
=> x3 +x^2y+xy^2-x^2y-y^2x- y3
=>x3-y3
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L.H.S
=>x3-y3
L.H.S = R.H.S
Hence VERIFIED✔✔
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HOPE IT HELPS U✌✌

Answer 2

Hey there !

We have to prove that x³ - y³ = (x-y)(x² + xy + y²)

So, Let's take R. H. S and prove it equal to L.H. S.

R. H. S

= (x-y)(x² + xy + y²)

= x ( x² + xy + y² ) - y ( x² + xy + y²)

= x³ + x²y + xy² -yx² -xy² - y³

= $x^3 + \cancel{ x^2 y } + \cancel{ x y^2 } - \cancel{ x^2 y } - \cancel{ x y^2 } -y^3$

= x³ - y³

= L. H. S.

$\mathbf{ Therefore \: , \: We \: proved \: that } \\ \boxed{x^3 - y^3 = (x-y)(x^2 + xy + y^2 ) \: }$