Question

what must be added to 2x²y² - 5x + 7 to get the sum -5x²y² + 7x -9?​

Answer 1

$\huge\boxed{\fcolorbox{purple}{ink}{Answer}}$

Let

the polynomial which should be added =x

ATQ

$\qquad\quad {:}\longmapsto\sf 2x^2y^2-5x+7+x=-5x^2y^2+7x-9$

Simplify

$\qquad\quad {:}\longmapsto\sf 2x^2y^2-5x+x+7=-5x^2y^2+7x-9$

$\qquad\quad {:}\longmapsto\sf 2x^2y^2-4x+7=-5x^2y^2+7x-9$

Interchange sides

Take unknown factors to left side and constants to right side

$\qquad\quad {:}\longmapsto\sf 2x^2y^2+5x^2y^2-4x-7x=-9-7$

$\qquad\quad {:}\longmapsto\sf 7x^2y^2-11x=-16$

Simplify

$\qquad\quad {:}\longmapsto\sf 7x^2y^2+16=11x$

$\qquad\quad {:}\longmapsto\sf x={\dfrac {7x^2y^2+16}{11}}$

Answer 2

Answer:

-7x²y² + 12x - 18 is the answer