Verify (x - y) (x² + xy + y²) = x^3 - y^3 by choosing different values of x and y. Class 9

Verify (x - y) (x² + xy + y²) = x³ - y³ by choosing different values of x and y. Class 9

Question 1.

Verify (x - y) (x² + xy + y²) = x³ - y³ by choosing different values of x and y. Class 9

Answer:

i. x= 5, y = 0:

(x - y) (x² + xy + y²)

= (5 - 0) (5² + (5)(0) + 0²)

= 5(25 + 0 + 0)

= 125

x³ - y³ = 5³ - 0³

= 125 - 0 = 125

ii. x= 3, y = 2:

(x - y) (x² + xy + y²)

= (3 - 2) (3² + (3)(2) + 2²)

= 1(9+ 6+ 4)

= 19

x³ - y³ = 3³ - 2³

= 27 - 8

= 19

∴ (x - y) (x² + xy + y²) = x³ - y³

[Note: Students can take other values of x and y and verify the identity.]

Question 2.

Predict what (x + y)(x² - xy + y²) will be. Class 9

Answer:

(x + y)(x² - xy + y²)

= x(x² - xy + y²) + y(x² - xy + y²)

= x³ - x²y + xy² + x²y - xy² + y³ = x³ + y³