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.
ScanSolve AI Answer
Welcome back MaMpangazitha — been a while! Let's pick up where you left off. Here are the solutions to your algebra problems. 1. Write down the constant term in each of these expressions: 1.a) 6x^2 - 10xy + 5 - 7y^3 The constant term is the term without any variables. The constant term is 5. 1.b) 12 + 4abc - 2ba + 13cd The constant term is the term without any variables. The constant term is 12. 1.c) 24m^3 + 12mn^3 - 33 - 60m^3 The constant term is the term without any variables. The constant term is -33. 2. Simplify where possible: 2.a) x^2 + y^2 These are not like terms, so the expression cannot be simplified further. The simplified expression is x^2 + y^2. 2.b) 3y^2 - 10y^2 Step 1: Combine the coefficients of the like terms (y^2). (3 - 10)y^2 Step 2: Perform the subtraction. -7y^2 The simplified expression is -7y^2. 2.c) 2x^2 + 9x - x^2 + 12x Step 1: Group like terms. (2x^2 - x^2) + (9x + 12x) Step 2: Combine the coefficients of the like terms. (2 - 1)x^2 + (9 + 12)x Step 3: Perform the operations. x^2 + 21x The simplified expression is x^2 + 21x. 2.d) 15ab + ab Step 1: Combine the coefficients of the like terms (ab). Remember ab is 1ab. (15 + 1)ab Step 2: Perform the addition. 16ab The simplified expression is 16ab. 2.e) 3ab + 4b - 6b - 7ab + 5c Step 1: Group like terms. (3ab - 7ab) + (4b - 6b) + 5c Step 2: Combine the coefficients of the like terms. (3 - 7)ab + (4 - 6)b + 5c Step 3: Perform the operations. -4ab - 2b + 5c The simplified expression is -4ab - 2b + 5c. 2.f) 10x^2y^3 - 5x^2y^3 Step 1: Combine the coefficients of the like terms (x^2y^3). (10 - 5)x^2y^3 Step 2: Perform the subtraction. 5x^2y^3 The simplified expression is 5x^2y^3. Drop the next question!