Question

"Question 9 Verify:
(i) x^3 + y^3 = (x+y)(x^2 - xy + y^2)
(ii) x^3 - y^3 = (x-y)(x^2 + xy + y^2)

Class 9 - Math - Polynomials Page 49"

Answer 1

Solution:

(i) x³ + y³ =(x + y)(x² –xy+y²)

We know that,

(x + y)³ = x³ + y³ + 3xy(x + y)

⇒ x³ + y³ = (x + y)³ – 3xy(x + y)

⇒ x³ + y³ = (x + y)[(x + y)² – 3xy]   

{Taking (x+y) Common}

⇒ x³+ y³= (x + y)[(x²+ y² + 2xy) – 3xy]

⇒ x³+ y³ = (x + y)(x² + y² – xy)

L.H.S = R.H.S

 

(ii) x³ – y³ = (x – y) (x² + xy + y² )

We know that,

(x – y)³ = x³ – y³ – 3xy(x – y)

⇒ x³ – y³ = (x – y)³ + 3xy(x – y)

⇒ x³ + y³ =(x – y)[(x – y)² + 3xy] 

{Taking (x-y) common}

⇒ x³ + y³= (x – y)[(x² + y² – 2xy) + 3xy]

⇒ x³+ y³ = (x + y)(x² + y² + xy)

L.H.S = R.H.S

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Hope this will help you.....

Answer 2

Hi

here is your answer

RHS

( x + y ) ( x² - xy + y² )

= x³ - x²y + xy² - xy² + x²y + y³

= x³ + y³

= LHS

===================================

ii ) RHS

( x + y ) ( x² - xy + y² )

= x³ - x²y + xy² + x²y - xy² + y³

= x³ + y³

= LHS

Hopes I helped.