MCR 3U1 UNIT 2: EQUIVALENT ALGEBRAIC EXPRESSIONS 2-1: Adding and Subtracting Polynomials Recall: . Like terms have the same variable raised to the same exponent. Only like terms can be added and subtracted when simplifying. . To add and subtract polynomials, you need to collect all like terms (by adding and subtracting their coefficients). EXAMPLE 1: Simplify. a) 6x' + 12x+5x2 -18x b) (2xy + 3x -4y?) +(6x-12y? -6xy) -(7y' +8xy + 5x) EXAMPLE 2: Michelle owns a company that sells gift wrap and cards. The function R(x) = -9x + 60x +1450 models her company's revenue, for *weeks. The function C(x) = 2x* -10x + 25 models the company's production costs. a) Write the simplified form of the profit function, P(x) = R(x) -C(x). b) How much profit will the company make after 4 weeks? Two polynomial expressions are equivalent if they simplify algebraically to give the same expression or if they produce the same graph. Two polynomial expressions are not equivalent if they result in different values when they are evaluated with the same numbers substituted for the variable(s). EXAMPLE 3: Use two different methods to show that P(t) = (-71* + 21 -4) + (6+31) and q(1) =(31 +7)-(5-212 + 21) are not equivalent algebraic functions