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
Here's the solution to 5(a): 5. (a) Simplify -3(2y^2 - 7) + 8(3y^2 - 12) and state: (i) the coefficient of y^2 (ii) the number of terms (iii) the constant term Step 1: Distribute the constants into the parentheses. -3(2y^2 - 7) + 8(3y^2 - 12) = (-3)(2y^2) + (-3)(-7) + (8)(3y^2) + (8)(-12) = -6y^2 + 21 + 24y^2 - 96 Step 2: Combine like terms. Group the y^2 terms and the constant terms. = (-6y^2 + 24y^2) + (21 - 96) = 18y^2 - 75 Now, let's state the required information from the simplified expression 18y^2 - 75: (i) The coefficient of y^2: This is the number multiplying y^2. The coefficient of y^2 is 18. (ii) The number of terms: Terms are separated by addition or subtraction. The terms are 18y^2 and -75. The number of terms is 2. (iii) The constant term: This is the term without any variables. The constant term is -75.