Question

Expand and simplify (r+5)(r+6)(4r-3)

Answer 1

To expand and simplify the expression (r+5)(r+6)(4r-3), use the distributive property and FOIL method. The expanded and simplified form is 4r^3 + 41r^2 + 87r - 90.

Step-by-step explanation:

To expand and simplify the expression (r+5)(r+6)(4r-3), we can use the distributive property and FOIL method.

1. First, distribute the first two terms of the expression (r+5)(r+6):
   • (r+5)(r+6) = r(r) + r(6) + 5(r) + 5(6) = r^2 + 6r + 5r + 30 = r^2 + 11r + 30.
2. Next, distribute this result with the third term (4r-3):
   • (r^2 + 11r + 30)(4r-3) = 4r(r^2) -3(r^2) + 4r(11r) -3(11r) + 4r(30) -3(30) = 4r^3 - 3r^2 + 44r^2 - 33r + 120r - 90 = 4r^3 + 41r^2 + 87r - 90.

Therefore, the expanded and simplified form of (r+5)(r+6)(4r-3) is 4r^3 + 41r^2 + 87r - 90.