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What should be added to 5x²y – 6xy + 8 to give you a sum of 3x²y -10xy +1?​

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ADDING POLYNOMIALS

Question: What should be added to 5x²y – 6xy + 8 to give you a sum of 3x²y -10xy +1?​

Representation:

Let [tex]z[/tex] be the unknown number.

Equation:

[tex]{\tt{(5x^{2}-6xy+8)+z=3x^{2} y-10xy+1 }}[/tex]

Solution (solve for z):

[tex]{\tt{(5x^{2} y-6xy+8)+z=3x^2y-10xy+1}}\\{\tt{-6xy+8+z=3x^{2}y-10xy+1-5x^{2} y}}\\{\tt{8+z=3x^{2} y-10xy+1-5x^{2} y+6xy}}\\{\tt{z=3x^{2} y-10xy+1-5x^{2} y+6xy-8}}\\{\tt{z=-2x^{2} y-10xy+1+6xy-8}}\\{\tt{z=-2x^{2} y-4xy+1-8}}\\{\boxed{\tt{z=-2x^{2} y-4xy-7}}}[/tex]

Answer:

[tex]{\orange{\boxed{\orange{\huge{\boxed{\sf{-2x^{2} y-4xy-7}}}}}}}[/tex]

Checking:

[tex]{\tt{(5x^{2} y-6xy+8)+(-2x^{2} y-4xy-7)}}\\{\tt{5x^{2} y-6xy+8-2x^{2} y-4xy-7}}\\{\tt{3x^{2} y-6xy+8-4xy-7}}\\{\tt{3x^{2} y-10xy+8-7}}\\{\boxed{\tt{3x^{2} y-10xy+1}}}[/tex]

[tex]{\blue{\boxed{ItzyMidzy:))}}}[/tex]

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