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Verify x^3-y^3=(x y)(x^2 y^2 xy)?
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Verify x^3-y^3=(x y)(x^2 y^2 xy)?
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Verify x^3-y^3=(x y)(x^2 y^2 xy)?
Verification of x^3-y^3=(xy)(x^2y^2+xy)



  • First, we will simplify the right-hand side of the equation by factoring out the common factor of xy:



    • xy(x^2y + 1)



  • Next, we will use the difference of cubes formula, which states that:



    • a^3 - b^3 = (a - b)(a^2 + ab + b^2)



  • Using this formula, we can rewrite the left-hand side of the equation as:



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



  • Substituting this expression into the original equation, we get:



    • (x - y)(x^2 + xy + y^2) = xy(x^2y + 1)



  • Expanding both sides of the equation:



    • x^3 - y^3 + x^2y^2 - xy^3 + xy^3 + x^2y - xy^2 = x^3y + xy

    • x^3 - y^3 + x^2y^2 + x^2y - xy^2 = x^3y + xy

    • x^3 - y^3 = xy(x^2y^2 + xy)



  • Therefore, we have verified that x^3-y^3=(xy)(x^2y^2+xy).

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