3.2 Adding, Subtracting and Multiplying Polynomials

Notes

• Add/subtract: combine like terms. When subtracting, distribute the minus sign to every term.
• Multiply: multiply every term in the first by every term in the second, then combine like terms.
• Useful patterns: $(a + b)^2 = a^2 + 2ab + b^2$, $(a - b)(a + b) = a^2 - b^2$, $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$.
• Example: $(x - 1)(x^2 + x + 1) = x^3 + x^2 + x - x^2 - x - 1 = x^3 - 1$.