Progress: Match the polynomial on the left with the simplified polynomial on the right. Qutation ID: 1 {:[{:(4x^(2)y-5xy^(2)+2x^(2)y^(2)+2xy)+(2x^(2)y+4xy+2xy^(2)-2x^(2)y^(2))}quad-6x^(2)y-3x^(2)y^(2)+2xy^(2)-2y],[-6x^(2)y^(2)+4x^(2)y-2xy^(2)+2x-2y],[(18x^(3)y^(2)+9x^(2)y^(3)-12x^(3)y^(3)+6xy^(2))/(3xy)],[{:[6x^(2)y^(2)+3x^(2)y-7xy-2xy^(2)+2y],[6x^(2)y-3xy^(2)+6xy]:}]:} Clear

Combine Like Terms: First, let's simplify the polynomial expression on the left by combining like terms. We have: (4x^2y - 5xy^2 + 2x^2y^2 + 2xy) + (2x^2y + 4xy + 2xy^2 - 2x^2y^2) - 6x^2y - 3x^2y^2 + 2xy^2 - 2y Combine like terms: (4x^2y + 2x^2y - 6x^2y) + (-5xy^2 + 2xy^2 + 2xy^2) + (2x^2y^2 - 2x^2y^2 - 3x^2y^2) + (2xy + 4xy) - 2y Now, simplify each group: (4x^2y + 2x^2y - 6x^2y) = 0 (-5xy^2 + 2xy^2 + 2xy^2) = -1xy^2 (2x^2y^2 - 2x^2y^2 - 3x^2y^2) = -3x^2y^2 (2xy + 4xy) = 6xy And we have -2y as it is. So, the simplified polynomial is: 0 - 1xy^2 - 3x^2y^2 + 6xy - 2y Which simplifies further to: -xy^2 - 3x^2y^2 + 6xy - 2y

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Progress: $\newline$ Match the polynomial on the left with the simplified polynomial on the right. $\newline$ Quotation ID: $1$ $\newline$ $\left\{\begin{array}{l} \left(4x^{2}y-5xy^{2}+2x^{2}y^{2}+2xy\right)+\left(2x^{2}y+4xy+2xy^{2}-2x^{2}y^{2}\right) - 6x^{2}y-3x^{2}y^{2}+2xy^{2}-2y \ -6x^{2}y^{2}+4x^{2}y-2xy^{2}+2x-2y \ \frac{18x^{3}y^{2}+9x^{2}y^{3}-12x^{3}y^{3}+6xy^{2}}{3xy} \ \left\{\begin{array}{l} 6x^{2}y^{2}+3x^{2}y-7xy-2xy^{2}+2y \ 6x^{2}y-3xy^{2}+6xy \end{array}\right. \end{array}\right.$ $\newline$ Clear

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Algebra 2

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Q. Progress:

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Match the polynomial on the left with the simplified polynomial on the right.

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Quotation ID:

1

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\left\{\begin{array}{l} \left(4x^{2}y-5xy^{2}+2x^{2}y^{2}+2xy\right)+\left(2x^{2}y+4xy+2xy^{2}-2x^{2}y^{2}\right) - 6x^{2}y-3x^{2}y^{2}+2xy^{2}-2y \ -6x^{2}y^{2}+4x^{2}y-2xy^{2}+2x-2y \ \frac{18x^{3}y^{2}+9x^{2}y^{3}-12x^{3}y^{3}+6xy^{2}}{3xy} \ \left\{\begin{array}{l} 6x^{2}y^{2}+3x^{2}y-7xy-2xy^{2}+2y \ 6x^{2}y-3xy^{2}+6xy \end{array}\right. \end{array}\right.

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Clear

Combine Like Terms: First, let's simplify the polynomial expression on the left by combining like terms. $\newline$ We have: $\newline$ $(4x^2y - 5xy^2 + 2x^2y^2 + 2xy) + (2x^2y + 4xy + 2xy^2 - 2x^2y^2) - 6x^2y - 3x^2y^2 + 2xy^2 - 2y$ $\newline$ Combine like terms: $\newline$ $(4x^2y + 2x^2y - 6x^2y) + (-5xy^2 + 2xy^2 + 2xy^2) + (2x^2y^2 - 2x^2y^2 - 3x^2y^2) + (2xy + 4xy) - 2y$ $\newline$ Now, simplify each group: $\newline$ $(4x^2y + 2x^2y - 6x^2y) = 0$ $\newline$ $(-5xy^2 + 2xy^2 + 2xy^2) = -1xy^2$ $\newline$ $(2x^2y^2 - 2x^2y^2 - 3x^2y^2) = -3x^2y^2$ $\newline$ $(2xy + 4xy) = 6xy$ $\newline$ And we have $-2y$ as it is. $\newline$ So, the simplified polynomial is: $\newline$ $0 - 1xy^2 - 3x^2y^2 + 6xy - 2y$ $\newline$ Which simplifies further to: $\newline$ $-xy^2 - 3x^2y^2 + 6xy - 2y$