Question

What should be taken away from
3x²- 4 y² + 5 xy + 20 to get -x² - y² + 6xy + 20​

Answer 1

Given :

⬤ 3x²- 4y² + 5xy + 20 to get -x² - y² + 6xy + 20

To Find :

⬤ Expression .

Solution :

$\bf\begin{gathered}:\implies{{3x}^{2}-{4y}^{2}+5xy+20-(?) = -{x}^{2}-{y}^{2}+6xy+20}\\ \\\end{gathered}$

Now :

$\sf\begin{gathered}:\implies{{3x}^{2}-{4y}^{2}+5xy+20-(-{x}^{2}-{y}^{2}+6xy+20)}\\ \\\end{gathered}$

$\sf\begin{gathered}:\implies{{3x}^{2}-{4y}^{2}+5xy+20+{x}^{2}+{y}^{2}-6xy-20}\\ \\\end{gathered}$

Combining Like Terms :-

$\sf\begin{gathered}:\implies{{(3x}^{2}+{x}^{2})+{(-4y}^{2}+{y}^{2})+(5xy+6xy)+(20-20)}\\ \\\end{gathered}$

$\sf\begin{gathered}:\implies{{4x}^{2}+{(3y}^{2})+(-xy)+0}\\ \\\end{gathered}$

$\bf\begin{gathered}:\implies{{4x}^{2}-{3y}^{2}-xy}\\ \\\end{gathered}$

Therefore , The Answer is 4x² - 3y² - xy .