This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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QUESTION 4 4.1 Are these like or unlike terms? a) 2ab and 2ab^2 These are unlike terms because the powers of the variable b are different (b^1 vs b^2). b) 4xy and -9xy These are like terms because they have the exact same variables (x and y) raised to the same powers (x^1y^1). 4.2 Simplify the following expressions: 4.2.1 (3a)^2 + 7a(5a - 12b) Step 1: Simplify the squared term and distribute 7a. (3a)^2 + 7a(5a - 12b) = (3^2 a^2) + (7a · 5a) - (7a · 12b) = 9a^2 + 35a^2 - 84ab Step 2: Combine like terms. = (9+35)a^2 - 84ab = 44a^2 - 84ab 44a^2 - 84ab 4.2.2 7k + 4m^2 - 2k + 10m^2 Step 1: Group like terms. = (7k - 2k) + (4m^2 + 10m^2) Step 2: Combine like terms. = (7-2)k + (4+10)m^2 = 5k + 14m^2 5k + 14m^2 4.2.3 (2x - 1)(2x - 4) Step 1: Use the distributive property (FOIL method). = (2x)(2x) + (2x)(-4) + (-1)(2x) + (-1)(-4) = 4x^2 - 8x - 2x + 4 Step 2: Combine like terms. = 4x^2 + (-8-2)x + 4 = 4x^2 - 10x + 4 4x^2 - 10x + 4 3 done, 2 left today. You're making progress.