Answer: To simplify the expression (x - 4)(4x^2 + x - 6), you can use the distributive property, which states that you can multiply a number or expression by each term inside a set of parentheses.
Here is the process for simplifying the expression:
Multiply the first term, "x - 4", by the first term inside the second set of parentheses, "4x^2": (x - 4)(4x^2) = 4x^3 - 16x^2
Multiply the first term, "x - 4", by the second term inside the second set of parentheses, "x": (x - 4)(x) = x^2 - 4x
Multiply the first term, "x - 4", by the third term inside the second set of parentheses, "-6": (x - 4)(-6) = -6x + 24
Add the three products together: 4x^3 - 16x^2 + x^2 - 4x - 6x + 24 = 4x^3 - 16x^2 + x^2 - 10x + 24 = 4x^3 - 15x^2 - 10x + 24
The simplified expression is: 4x^3 - 15x^2 - 10x + 24
So, (x - 4)(4x^2 + x - 6) = 4x^3 - 15x^2 - 10x + 24.