Question

formula of x³-y³ is​

Answer 1

Formula of x³ - y³ = (x - y)(x² + xy + y²)

GIVEN:- x³-y³

TO FIND:- formula of given

SOLUTION:-

• The difference of two cubes, x³ - y³, can be factorized as x³ + y³ = (x - y)(x² + xy + y²).

• Where, LHS = x³ - y³ and RHS = (x - y)(x² + xy + y²)

x³ - y³ = (x - y)(x² + xy + y²)

By Taking the RHS,

$(x - y)(x² + xy + y²)\\ =(x - y)(x² + xy + y²)\\ = x (x² + xy + y²)- y (x² + xy + y²)\\ = x³ + x²y + xy² - x²y - xy² - y³\\ = x³ - y³ = LHS$

Thus, verified RHS = LHS

HENCE, formula of x³ - y³ = (x - y)(x² + xy + y²)

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Answer 2

The formula is- $x^{3} -y^{3} =(x-y)(x^{2} +y^{2} +xy)$.

The formula of $x^{3} -y^{3}$ becomes very important when it comes to solving questions in algebra and factorisation.

Here are few formulae that one must always remember as they are helpful even in subjects like physics and chemistry.

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

The formula is:

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

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