Add, subtract, and multiply polynomials · lesson

Adding and subtracting polynomials

💡 Combine like terms by degree, and when subtracting, change the sign of every term in the second polynomial.

Like terms have the same variable and the same exponent. x² terms combine only with x² terms.

When subtracting a polynomial, distribute the minus sign to every term in it first.

Write the answer from highest power to lowest.

🧠 Let's work it out

Find (4x² + x) − (x² − 3x + 2).

What do you think comes next?

💡 To multiply polynomials, multiply each term of the first by each term of the second, then combine like terms.

A monomial times a polynomial: multiply it by each term. Add exponents when you multiply powers of x.

A binomial times a trinomial: each of the 2 terms multiplies each of the 3 terms, making 6 products. Then combine.

🧠 Let's work it out

Find (x + 2)(x² − x + 4).

What do you think comes next?

💡 Multiply first, outer, inner, and last terms, then combine the two middle terms.

(a + b)(c + d) has four products: first, outer, inner, last. People call it FOIL.

The outer and inner products are usually like terms. Combine them into one middle term.

Carry the signs with each term.

🧠 Let's work it out

Find (2x + 3)(x − 1).

What do you think comes next?

💡 (a + b)² = a² + 2ab + b², and (a − b)(a + b) = a² − b².

A binomial squared is the binomial times itself. The middle term is twice the product of the two terms. Don't just square each term.

(a − b)(a + b) has middle terms that cancel. Only a² − b² is left.

🧠 Let's work it out

Find (x + 5)².

What do you think comes next?