Question

Which is true about the degree of the sum and difference of the polynomials 3x5y – 2x3y4 – 7xy3 and –8x5y + 2x3y4 + xy3?

Answer 1

Let us consider the polynomials $3x^5y-2x^3y^4-7xy^3$ and $-8x^5y+2x^3y^4+xy^3$.

The sum of the given polynomials is:

= $3x^5y-2x^3y^4-7xy^3+[-8x^5y+2x^3y^4+xy^3]$

= $-5x^5y-6xy^3$

Hence, the degree of sum of the given polynomials is '6'.

Consider the difference of the given polynomials,

$3x^5y-2x^3y^4-7xy^3-[-8x^5y+2x^3y^4+xy^3]$

= $3x^5y-2x^3y^4-7xy^3+8x^5y-2x^3y^4-xy^3$

=$11x^5y-4x^3y^4-8xy^3$

The degree of the difference of the given polynomials is '7'.