Question

Perform the indicated operations. Indicate the degree of the resulting polynomial. (13x3y2−5x2y−9x2)−(−11x3y2−6x2y+3x2−$$4)(13x^3y^2$-5x^2y-9x^2$)-(-11x^3y^2$-6x^2$y+3x^2-4)$$

Accepted Answer

Rewrite the expression by distributing the negative sign to the second polynomial: $$ (13x$$^{3}$$y^{2}$$ - $$5x^{2}y$$ - $$9x^{2}$$) - $$(-11x^{3}y$$^{2}$$ - 6x$$^{2}$$y + 3x$$^{2}$$ - 4) $$ becomes $$ 13x$$^{3}$$y^{2}$$ - $$5x^{2}y$$ - $$9x^{2}$$ + $$11x^{3}y$$^{2}$$ + 6x$$^{2}$$y - 3x$$^{2}$$ + 4 . $$Group like terms together. Combine the terms with $$x^{3}y$$^{2}$$, the terms with x$$^{2}$$y$$, the terms with $$x^{2}$$, and the constant term: $$ (13x$$^{3}$$y^{2}$$ + $$11x^{3}y$$^{2}$$) + (-5x$$^{2}$$y + 6x$$^{2}$$y) + (-9x$$^{2}$$ - 3x$$^{2}$$) + 4 . $$Add or subtract the coefficients of the like terms: $$ (13 + 11)x$$^{3}$$y^{2} + (-5$$ + $$6)x^{2}y + (-9$$ - $$3)x^{2} + 4$$ $$. Write the simplified polynomial after combining like terms: $$ $$24x^{3}y$$^{2}$$ + 1x$$^{2}$$y - 12x$$^{2}$$ + 4 . $$Determine the degree of the resulting polynomial by finding the term with the highest sum of exponents. For example, for $$x^{3}y$$^{2}$$, the degree is 3 + 2 = 5$. Compare this with the degrees of other terms to identify the highest degree.

Perform the indicated operations. Indicate the degree of the resulting polynomial. $(13 x^{3} y^{2} - 5 x^{2} y - 9 x^{2}) - (- 11 x^{3} y^{2} - 6 x^{2} y + 3 x^{2} - 4)$

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Key Concepts

Polynomial Operations (Addition and Subtraction)

Like Terms and Combining Like Terms

Degree of a Polynomial

Perform the indicated operations. Indicate the degree of the resulting polynomial. (13x3y2−5x2y−9x2)−(−11x3y2−6x2y+3x2−4)(13x^3y^2-5x^2y-9x^2)-(-11x^3y^2-6x^2y+3x^2-4)