Question

verify that :


x³+y²=(x+y)(x²+y²-xy)​

Answer 1

$\huge\mathfrak{Solution}$

[Correction : x³+y³=(x+y)(x²+y²-xy) ]

x³+y³=(x+y)(x²+y²-xy)

Taking RHS,

(x+y)(x²+y²-xy)

By multiplying horizontally,

x(x²+y²-xy)+y(x²+y²-xy)

x²+xy²-x²y+x²y+y³-xy²

The similar positive and negative values are cancelled out,

Therefore, result will be :

x³+y³ = x³+y²

LHS = RHS

Hence verified!

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Thanks Ω

Answer 2

Steps Are Given Below:-

• $\fbox {RHS}$

$= > (x + y)(x {}^{2} + {y}^{2} - xy) \\ = > (x)(x {}^{2} ) + (x)( {y}^{2} ) - (x)(xy) + y( {x}^{2} ) + \\ y( {y}^{2} ) - y(xy) \\ = > {x}^{3} + x {y}^{2} - {x}^{2} y + {x}^{2} y + {y}^{3} - x{y}^{2} \\ = > {x}^{3} + {y}^{3} + xy {}^{2} - x{y}^{2} + {x}^{2} y - {x}^{2} y \\ = > x {}^{3} + {y}^{3} + 0 + 0 \\ = > {x}^{3} + {y}^{3}$

Point to Note

$there \: is \: y {}^{3} \: not \: {y}^{2}$