x³+ y³ = (x + y) (x² - xy + y²)
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x³± y³ = (x ± y) (x² ± xy + y²) -—»
We can Prove this true.. if you Want to derive it Just do The Things of Proof Opposite
PROOF :
x³+ y³ = (x + y) (x² - xy + y²)
TAKING RHS
(x + y) (x² - xy + y²)
x(x²-xy+y²)+y(x²-xy+y²)
x³-x²y+xy²+x²y-xy²+y³
=x³+y³
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x³- y³ = (x - y) (x² + xy + y²)
TAKING RHS
(x-y)(x²+xy+y²)
x(x²+xy+y²)-y(x²+xy+y²)
x³+x²y-xy²-x²y+xy²-y³
=x³-y³
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DERIVATION :
x³+y³
ADD AND SUBTRACT (x²y+xy²)
x³+x²y-xy²-x²y+xy²+y³
x(x²-xy+y²)+y(x²-xy+y²)
(x + y) (x² - xy + y²)
x³-y³
ADD AND SUBTRACT (x²y+xy²)
x³+x²y-xy²-x²y+xy²+y³
x(x²+xy+y²)-y(x²+xy+y²)
(x-y)(x²+xy+y²)
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Hope it Helps
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