62.6k views
1 vote
I hate polynomials so much thank you for your help!

I hate polynomials so much thank you for your help!-example-1
User Dave Amit
by
8.0k points

1 Answer

2 votes

Solution:

Given the polynomials below;

For the first polynomial


\left(5xy^2-3x^2y-2x+3xy\right)+\left(3xy^2+4x-5xy+2x^2y\right)

Adding the polynomials gives


\begin{gathered} \left(5xy^2-3x^2y-2x+3xy\right)+\left(3xy^2+4x-5xy+2x^2y\right)= \\ =5xy^2-3x^2y-2x+3xy+3xy^2+4x-5xy+2x^2y \\ \mathrm{Group\:like\:terms} \\ =5xy^2+3xy^2-3x^2y+2x^2y-2x+4x+3xy-5xy \\ =8xy^2-x^2y+2x-2xy \end{gathered}

Hence, the matching polynomial is


8xy^2-x^2y+2x-2xy

For the second polynomial


\left(4x^2y-3xy^2+4x-3xy\right)-\left(-4x^2y+2xy+3xy^2+x\right)

Subtracting the polynomials gives


\begin{gathered} \left(4x^2y-3xy^2+4x-3xy\right)-\left(-4x^2y+2xy+3xy^2+x\right) \\ =4x^2y-3xy^2+4x-3xy-\left(-4x^2y+2xy+3xy^2+x\right) \\ =4x^2y-3xy^2+4x-3xy+4x^2y-2xy-3xy^2-x \\ \mathrm{Group\:like\:terms} \\ =8x^2y-6xy^2+3x-5xy \end{gathered}

Hence, the matching polynomial is


8x^2y-6xy^2+3x-5xy

For the third polynomial


\left(2x-1\right)\left(4xy+3y^2-2y\right)

Multiplying the polynomials


\begin{gathered} =2x(\:4xy)+2x(3y^2)+2x\left(-2y\right)-1(\:4xy)-1(\:3y^2)-1\left(-2y\right) \\ =8x^2y+6xy^2-8xy-3y^2+2y \end{gathered}

Hence, the matching polynomial is


\begin{equation*} 8x^2y+6xy^2-8xy-3y^2+2y \end{equation*}

For the fourth polynomial


(16x^2y^3-2x^3y^2+4x^2y^2+4xy)/(2xy)

Dividing the polynomials


\begin{gathered} (16x^2y^3-2x^3y^2+4x^2y^2+4xy)/(2xy) \\ =(2xy\left(8xy^2-x^2y+2xy+2\right))/(2xy) \\ =8xy^2-x^2y+2xy+2 \end{gathered}

Hence, the matching polynomial is


\begin{equation*} 8xy^2-x^2y+2xy+2 \end{equation*}

User Nathaniel Elkins
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories