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Chapter 0: Problem 29

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

Short Answer

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

Step by step solution

01

Distribute the First Term

Multiply the first term of the first polynomial to each term of the second polynomial to get: \(8 x^{3}x^{2}-8 x^{3}*5\)
02

Distribute the Second Term

Next, multiply the second term of the first polynomial to each term of the second polynomial to get: \(3x^{2}-3*5\)
03

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

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