Add and subtract polynomials

Learning Objectives Identify monomials and polynomials. Identify like terms within a polynomial expression. Combine like terms to simplify polynomial expressions. Add polynomials by combining like terms. Subtract polynomials by distributing the negative sign and combining like terms. Simplify expressions involving both addition and subtraction of polynomials. Solve real-world problems involving the addition and subtraction of polynomials. Ever wondered how engineers calculate the total cost of materials for a complex structure, or how scientists model population growth over time? 🤔 In this lesson, you'll learn how to add and subtract polynomials, which are powerful mathematical expressions used to describe many real-world situations. Mastering this skill will help y...

TermDefinitionExample MonomialA single term that is a number, a variable, or a product of numbers and variables with whole number exponents.5x², 7, y, -3xy³ PolynomialAn expression consisting of one or more monomials added or subtracted.3x² + 2x - 5 TermEach monomial in a polynomial, separated by addition or subtraction signs.In 3x² + 2x - 5, the terms are 3x², 2x, and -5. CoefficientThe numerical factor of a term.In 3x², the coefficient is 3. In 2x, the coefficient is 2. In -y, the coefficient is -1. Constant TermA term that has no variable part; it is just a number.In 3x² + 2x - 5, the constant term is -5. Like TermsTerms that have the same variables raised to the same powers. Only their coefficients can be different.4x² and -7x² are like terms. 5xy and 2xy are like terms. 3x and 3x² ar...

Combining Like Terms $ax^n + bx^n = (a+b)x^n$ To combine like terms, add or subtract their coefficients while keeping the variable part (variables and their exponents) exactly the same. This rule is fundamental for simplifying polynomials. Adding Polynomials $(P_1) + (P_2) = P_1 + P_2$ (then combine like terms) To add polynomials, simply remove the parentheses and then combine all like terms present in the expression. The signs of the terms remain unchanged. Subtracting Polynomials $(P_1) - (P_2) = P_1 + (-1 \cdot P_2)$ (then combine like terms) To subtract polynomials, distribute the negative sign to every term in the second polynomial (change the sign of each term inside the second parenthesis), then remove the parentheses, and finally combine all like terms. This...