Polynomials are basically addition or difference of more than one monomials. In Polynomials every monomial behaves as a single term of polynomial. Monomials are variable or real number which have a Whole Number exponent.

Let us see how to solve polynomials with exponents:

Condition 1: If we have a polynomial in form (x

Condition 2: If we have polynomials in form of (x

This is called Foil Method which is used to simplify multiplication of two polynomials. So these are two conditions which arise when we solve polynomials with exponents.

Let us see how to solve polynomials with exponents:

Condition 1: If we have a polynomial in form (x

^{2}y^{2})^{4}then this is a simple addition of exponents. Here 'x' and 'y' are two different variables which have exponent two over them, and exponent 4 is outside the parenthesis. In this condition we just simply and add exponents. When we add the exponents of 'x' we get x^{6}and when we add exponents of 'y' we get y6. We get solution x6y6 of polynomials.Condition 2: If we have polynomials in form of (x

^{2}+ y^{2})^{2}then there is a problem which arise in this condition. We cannot distribute exponent to polynomials because polynomials inside parenthesis are not being divided or multiplied by exponents. So we cannot distribute exponent to polynomials inside the parenthesis. In this condition we do not multiply the exponent and powers of polynomials but we multiply whole polynomial inside the parenthesis by the number of exponent. In this the exponent is 2 so will multiply the polynomial two times. (x^{2}+ y^{2}) (x^{2}+ y^{2}). This is how we multiply whole polynomial. We multiply whole polynomial with itself and then add them as x^{4}+ x^{2}y^{2}+ x^{2}y^{2}+ y^{4}= x^{4}+ 2 x^{2}y^{2}+ y4.This is called Foil Method which is used to simplify multiplication of two polynomials. So these are two conditions which arise when we solve polynomials with exponents.