Multiplication of polynomials

To multiply two polynomials we use the “each by each” rule: every term of the first must be multiplied by every term of the second. An arc diagram helps you not to forget any product.

Example — Arc diagram for multiplication

Let us multiply $(1+2a-a^2)\cdot(3-a)$. Every term of the first factor is joined by an arc to each term of the second:

Every term of the first factor must be multiplied by every term of the second: six partial products in all.

Adding the like terms together: $(1+2a-a^2)(3-a) = a^3 - 5a^2 + 5a + 3$

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Topics: Algebraic calculus
Concepts: Multiplication of polynomials · Polynomial
Skills: Calculating