How is multiplying polynomials different from adding them?

Answer 1

When you add polynomials, you combine only like terms together.

For example, (x^3+x^2)+(2x^2+x)= x^3+(1+2)x^2+x=x^3+3x^2+x

When you multiply polynomials, you multiply all pairs of terms together.

(x^2+x)(x^3+x)=(x^2)(x^3)+(x^2)(x)+(x)(x^3)+(x)(x)=x^5+x^3+x^4+x^2

Basically, in addition you look at like terms to simplify. In multiplication, you multiply each term individually with every term on the opposite side, ignoring like terms.