Question

What much bigger is $5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 10{{\text{x}}^2}{\text{y}}$ than $ - 5{{\text{x}}^2} + 6{{\text{x}}^2}{\text{y}} - 7{\text{xy}}$?

Answer 1

Hint: Subtract the second polynomial$\left( { - 5{{\text{x}}^2} + 6{{\text{x}}^2}{\text{y}} - 7{\text{xy}}} \right)$ from first polynomial$\left( {5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 10{{\text{x}}^2}{\text{y}}} \right)$ . The difference of the two polynomials tell us how much bigger the first polynomial is from other polynomials.

Complete step-by-step answer:
Given, first polynomial= $5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 10{{\text{x}}^2}{\text{y}}$
And, second polynomial= $ - 5{{\text{x}}^2} + 6{{\text{x}}^2}{\text{y}} - 7{\text{xy}}$
We have to find how much bigger the first polynomial is from the second polynomial. To find this, we have to find the difference between these two polynomials. Then,
First polynomial- second polynomial=difference of the polynomial
$ \Rightarrow $ $5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 10{{\text{x}}^2}{\text{y}}$$ - \left( { - 5{{\text{x}}^2} + 6{{\text{x}}^2}{\text{y}} - 7{\text{xy}}} \right) = $ Difference
Now open the bracket and multiply the sign inside the bracket-
$ \Rightarrow $ Difference=$5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 10{{\text{x}}^2}{\text{y}} + 5{{\text{x}}^2} - 6{{\text{x}}^2}{\text{y + }}7{\text{xy}}$
Now separate the common terms and simplify the eq.-
$ \Rightarrow $ Difference=$5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 10{{\text{x}}^2}{\text{y}} - 6{{\text{x}}^2}{\text{y}} + 5{{\text{x}}^2}{\text{ + }}7{\text{xy}}$
$ \Rightarrow $ Difference=$5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 16{{\text{x}}^2}{\text{y}} + 5{{\text{x}}^2}{\text{ + }}7{\text{xy}}$
So the first polynomial is $5{{\text{x}}^2}{{\text{y}}^2} - 18{\text{x}}{{\text{y}}^2} - 16{{\text{x}}^2}{\text{y}} + 5{{\text{x}}^2}{\text{ + }}7{\text{xy}}$ bigger than second polynomial.

Note: The student may go wrong when subtracting the polynomials if they subtract the coefficient of different terms. We should remember that coefficients of only the same terms can be subtracted the rest of the terms are written the same. Like the coefficient of ${{\text{x}}^2}{\text{y}}$ are subtracted because they have common term ${{\text{x}}^2}{\text{y}}$.The rest of the terms are written the same.