Question

Question 8

Out of the four options, only one is correct. Write the correct answer.

The sum of $x^4-xy+2y^2$ and $-x^4+xy+2y^2$ is

(a) monomial and polynomial in y
(b) binomial and polynomial
(c) trinomial and polynomial
(d) monomial and polynomial in x

Answer 1

Required sum $=(x^4-xy+2y^2)+(-x^4+xy+2y^2)$
$=x^4-xy+2y^2-x^4+xy+2y^2=\left[\right(x^4+(-x^4)\left)\right]+(-xy+xy)+(2y^2+2y^2)=0+0+4y^2=4y^2$
$4y^2$ is a monomial and polynomial in y.
Hence option (a) is correct.