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Chapter 0: Problem 30

Find each product. $$\left(7 x^{3}+5\right)\left(x^{2}-2\right)$$

Short Answer

Expert verified
\(7x^{5} - 14x^{3} + 5x^{2} - 10\)

Step by step solution

01

Distribute First Term of First Polynomial

First, distribute the first term of the first polynomial \(7x^{3}\) with each term in the second polynomial \((x^{2} - 2)\). This gives us: \(7x^{3} \cdot x^{2} - 7x^{3} \cdot 2\) which simplifies to \(7x^{5} - 14x^{3}\).
02

Distribute Second Term of First Polynomial

Next, distribute the second term of the first polynomial \(5\) with each term in the second polynomial \((x^{2} - 2)\). This gives us: \(5 \cdot x^{2} - 5 \cdot 2\) which simplifies to \(5x^{2} - 10\).
03

Combine Like Terms

Now, combine the results from Step 1 and Step 2 to obtain the final form of the expanded product. The final product is \(7x^{5} - 14x^{3} + 5x^{2} - 10\).

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