Question

Verify:x3+y= (x+y)(x2+xy+y?)​

Answer 1

To verify :

x³ + y³ = ( x + y )( x² - xy + y² )

Solution :

The term on the RHS is :

=> ( x + y )( x² - xy + y² )

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

=> x³ - x²y + xy² + x²y - xy² + y³

The common terms get cancelled leaving with -

=> x³ + y³ .

Therefore LHS = RHS

Hence Verified

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

Answer:

Correct Question :-

$\mapsto$ Verify : x³ + y³ = (x + y) (x² - xy + y²)

Solution :-

$\dashrightarrow$ L.H.S : x³ + y³

▪️We know that,

$\green\bigstar$ (x + y)³ = x³ + y³ + 3xy (x + y)

So, x³ + y³ = (x + y)³ - 3xy (x + y)

$\implies$ (x + y)³ - 3xy (x + y)

$\implies$ (x + y) [ (x + y)² - 3xy ]

▪️By using the formula,

$\red\bigstar$ (a + b)² = a² + b² + 2ab

$\implies$ (x + y) [ (x² + y² + 2xy) - 3xy ]

$\implies$ (x + y) (x² + y² - xy)

$\implies$ (x + y) (x² - xy + y²)

$\dashrightarrow$ R H.S

$\leadsto$ $\boxed{\bold{\large{Proved}}}$

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