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 $\boxed{18}$. (ii) The number of terms: Terms are separated by addition or subtraction. The terms are $18y^2$ and $-75$. The number of terms is $\boxed{2}$. (iii) The constant term: This is the term without any variables. The constant term is $\boxed{-75}$.