Question

answer this question
class 9 ​

Answer 1

Answer:

(i) Taking the RHS,

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

= x³ - x²y + xy² + x²y - xy² + y³

= x³ + y³ = LHS

ii) x³ - y³ = (x - y)(x² + xy + y²)

Taking the RHS,

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

= x³ + x²y + xy² - x²y - xy² - y³

= x³ - y³ = LHS

Hence, verified.

(I)photo answer

Answer 2

Step-by-step explanation:

$\sf (i) \: x^3+ y^3 = (x+y)(x^2-xy+y^2)$

Solution:-

$\sf LHS = {x}^{3} + {y}^3$

$\sf RHS = (x + y)( {x}^{2} - xy + {y}^{2} )$

$\implies \sf (x + y)( {x}^{2} - xy + {y}^{2} )$

${\implies \sf x( {x}^{2} - xy + {y}^{2} ) + y( {x}^{2} - xy + {y}^{2} )}$

${ \implies \sf {x}^{3 } - {x}^{2} y + x {y}^{2} + {x}^{2}y - x {y}^{2} + {y}^{3} }$

${ \implies \sf {x}^{3 } - {x}^{2} y+ {x}^{2}y + x {y}^{2} - x {y}^{2} + {y}^{3} }$

${ \implies \boxed{\sf {x}^{3} + {y}^{3} }}$

$\implies \sf LHS$

Hence, verified.

$\sf (ii) \: x^3 - y^3 = (x - y)(x^2 + xy+y^2)$

Solution:-

$\sf LHS = {x}^{3} - {y}^3$

$\sf RHS = (x - y)( {x}^{2} + xy + {y}^{2} )$

${\implies \sf x( {x}^{2} + xy + {y}^{2} ) - y( {x}^{2} + xy + {y}^{2} )}$

${\implies \sf x^{3} + {x}^{2} y + x{y}^{2} - {x}^{2}y - x {y}^{2} - {y}^{3} }$

${\implies \sf x^{3} + {x}^{2} y - {x}^{2}y+ x{y}^{2} - x {y}^{2} - {y}^{3} }$

$\implies \boxed{ \sf {x}^{3} - {y}^{3} }$

$\implies \sf LHS$

Hence, verified.