CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Application of Algebraic Identities

Question 9Ver...

Question

Question 9
Verify:
$(i) x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2}) (i i) x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})$

Open in App

Solution

$(i) x^{3} + y^{3} [u s i n g i d e n t i t y a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})] = (x + y) (x^{2} - x y + y^{2}) R . H . S . = x (x^{2} - x y + y^{2}) + y (x^{2} - x y + y^{2}) = x^{3} - x^{2} y + x y^{2} + y x^{2} - x y^{2} + y^{3} = x^{3} + y^{3} = L . H . S$

$(i i) x^{3} - y^{3} [u s i n g i d e n t i t y a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})] = (x - y) (x^{2} + x y + y^{2}) R . H . S . = x (x^{2} + x y + y^{2}) - y (x^{2} + x y + y^{2}) = x^{3} + x^{2} y + x y^{2} - y x^{2} - x y^{2} - y^{3} = x^{3} - y^{3} = L . H . S .$

Suggest Corrections

thumbs-up

29

Similar questions

Verify:

(i)

(ii)

x^{3} + y^{3} - (x + y) (x^{2} - x y + y^{2})

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

x^{3} + y^{3} = (x + y) (x^{2} + x y + y^{2})

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Application of Algebraic Identities

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon