Problem 29 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The answer is \(8x^{5} - 40x^{3} + 3x^{2} - 15\)

Step 1: Distribute the First Term

Multiply the first term of the first polynomial to each term of the second polynomial to get: \(8 x^{3}x^{2}-8 x^{3}*5\)

Step 2: Distribute the Second Term

Next, multiply the second term of the first polynomial to each term of the second polynomial to get: \(3x^{2}-3*5\)

Step 3: Simplify

Combine the results from steps 1 and 2. When doing this, remember to simplify any multiplication of exponents according to the power rule (which states that we add the exponents). This gives us: \(8x^{5} - 40x^{3} + 3x^{2} - 15\)