Problem 29 - College Algebra

Question

Find each product. $$\left(8 x^{3}+3\right)\left(x^{2}-5\right)$$

Step-by-Step Solution

Answer

\(8x^5\text{-}40x^3 + 3x^2\text{-}15\)

Step 1: Distribute \(8x^3\) over \(x^2\text{-}5\)

First, distribute the first term \(8x^3\) of the first binomial over the second binomial resulting in \(8x^3 \cdot x^2\text{-}8x^3 \cdot 5 = 8x^5\text{-}40x^3\)

Step 2: Distribute \(3\) over \(x^2\text{-}5\)

Next, distribute the second term \(3\) of the first binomial over the second binomial resulting in \(3 \cdot x^2\text{-}3\cdot 5 = 3x^2\text{-}15\)

Step 3: Combine like terms

Finally, combine like terms from step 1 and step 2 to get the final result: \(8x^5\text{-}40x^3 + 3x^2\text{-}15\)