Final answer:
To expand and simplify 1 - 4x(6x - 3y), distribute -4x across the parentheses to get -24x^2 + 12xy, then add the 1 to get the simplified expression -24x^2 + 12xy + 1.
Step-by-step explanation:
To expand and simplify the expression 1 - 4x(6x - 3y), we need to distribute the -4x across the terms inside the parentheses and then combine like terms.
- First, multiply -4x by 6x, which equals -24x2.
- Second, multiply -4x by -3y, which equals +12xy (remember that a minus times a minus is a plus).
Now, combine the terms to get the simplified expression: -24x2 + 12xy + 1.
To ensure we did it correctly, let's check if the expression looks reasonable:
- There are no like terms left to combine.
- The original expression is fully expanded.