Answer:
12 x^9 + 15 x^8 - 8 x^6 - 10 x^5 = A.) is the answer
Step-by-step explanation:
Expand the following:
x^4 (3 x^3 - 2) (4 x^2 + 5 x)
Hint: | Multiply 3 x^3 - 2 and 4 x^2 + 5 x together using FOIL.
(3 x^3 - 2) (4 x^2 + 5 x) = (3 x^3) (4 x^2) + (3 x^3) (5 x) + (-2) (4 x^2) + (-2) (5 x) = 12 x^5 + 15 x^4 - 8 x^2 - 10 x = 12 x^5 + 15 x^4 - 8 x^2 - 10 x:
x^4 12 x^5 + 15 x^4 - 8 x^2 - 10 x
Hint: | Distribute x^4 over 12 x^5 + 15 x^4 - 8 x^2 - 10 x.
x^4 (12 x^5 + 15 x^4 - 8 x^2 - 10 x) = x^4 (12 x^5) + x^4 (15 x^4) + x^4 (-8 x^2) + x^4 (-10 x):
12 x^4 x^5 + 15 x^4 x^4 - 8 x^4 x^2 - 10 x^4 x
Hint: | Combine products of like terms.
x^4 (-10) x = x^(4 + 1) (-10):
12 x^4 x^5 + 15 x^4 x^4 - 8 x^4 x^2 + -10 x^5
Hint: | Evaluate 4 + 1.
4 + 1 = 5:
12 x^4 x^5 + 15 x^4 x^4 - 8 x^4 x^2 - 10 x^5
Hint: | Combine products of like terms.
x^4 (-8) x^2 = x^(4 + 2) (-8):
12 x^4 x^5 + 15 x^4 x^4 + -8 x^6 - 10 x^5
Hint: | Evaluate 4 + 2.
4 + 2 = 6:
12 x^4 x^5 + 15 x^4 x^4 - 8 x^6 - 10 x^5
Hint: | Combine products of like terms.
x^4×15 x^4 = 15 x^8:
12 x^4 x^5 + 15 x^8 - 8 x^6 - 10 x^5
Hint: | Combine products of like terms.
x^4×12 x^5 = x^(4 + 5)×12:
12 x^9 + 15 x^8 - 8 x^6 - 10 x^5
Hint: | Evaluate 4 + 5.
4 + 5 = 9:
Answer: 12 x^9 + 15 x^8 - 8 x^6 - 10 x^5
