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Mathematics

x3y3x(y2+x2z2)x^3 - y^3 - x(y^2 + \overline{x^2 - z^2}) is equal to:

  1. y3 + xy2 + xz2

  2. y3 + xy2 - xz2

  3. -y3 + xy2 - xz2

  4. -y3 - xy2 + xz2

Algebraic Expressions

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Answer

x3y3x(y2+x2z2)x^3 - y^3 - x(y^2 + \overline{x^2 - z^2})

= x3y3x(y2+x2z2)x^3 - y^3 - x(y^2 + x^2 - z^2)

= x3y3xy2x3+xz2x^3 - y^3 - xy^2 - x^3 + xz^2

= (x3x3)y3xy2+xz2(x^3 - x^3) - y^3 - xy^2 + xz^2

= y3xy2+xz2- y^3 - xy^2 + xz^2

Hence, option 4 is the correct option.

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