Question

verify the identity x cube-y cube = (x-y) (x square+y square +xy)

Answer 1

We know that,

(a+b)³ = (a+b)²(a+b)

(a+b)³ = (a² + b² + 2ab)(a+b)

(a+b)³ = a(a² + b² + 2ab) +b(a² + b² + 2ab)

(a+b)³ = a³ + ab² + 2a²b + a²b + b³ +2ab²

(a+b)³ = a³ + b³ + 3ab² + 3a²b

We have find a³ + b³. therefore, transfer other terms to one side:

(a+b)³ - 3a²b - 3a²b = a³ + b³

a³ + b³ = (a+b)³ - 3a²b - 3a²b

a³ + b³ = (a+b)³ -3ab(a+b)

Taking (a+b) common,

a³ + b³ = (a+b){(a+b)² -3ab}

a³ + b³ = (a+b){a² + b² + 2ab -3ab}

a³ + b³ = (a+b)(a² + b² - ab)

Hence proved;

Note:-

(a+b)² = (a+b)(a+b)

= a(a+b) +b(a+b)

= a² + ab + ba + b²

= a² + b² + 2ab

Answer 2

Answer:

Step-by-step explanation:

x cube -y cube= (x-y)(x square +xy+y square)