To multiply the binomials \( (5x^3 + 6)(x^2 - 4) \) using the FOIL method, we'll follow the steps for each part of the method: First, Outside, Inside, Last.
-
First: Multiply the first terms. \[ 5x^3 \cdot x^2 = 5x^{3+2} = 5x^5 \]
-
Outside: Multiply the outer terms. \[ 5x^3 \cdot (-4) = -20x^3 \]
-
Inside: Multiply the inner terms. \[ 6 \cdot x^2 = 6x^2 \]
-
Last: Multiply the last terms. \[ 6 \cdot (-4) = -24 \]
Now, combine all these results together: \[ 5x^5 - 20x^3 + 6x^2 - 24 \]
Next, we will rearrange the terms in descending order of the exponent: \[ 5x^5 - 20x^3 + 6x^2 - 24 \]
Thus, the final answer after simplifying is: \[ \boxed{5x^5 - 20x^3 + 6x^2 - 24} \]
7 answers