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

Step by step solution

01

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 \(8x^3 \cdot x^2\text{-}8x^3 \cdot 5 = 8x^5\text{-}40x^3\)
02

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

Next, distribute the second term \(3\) of the first binomial over the second binomial resulting in \(3 \cdot x^2\text{-}3\cdot 5 = 3x^2\text{-}15\)
03

Combine like terms

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

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Most popular questions from this chapter

Explain the product rule for exponents. Use \(2^{3} \cdot 2^{5}\) in your explanation.

Evaluate each exponential expression in $$\frac{x^{14}}{x^{-7}}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right)$$

Will help you prepare for the material covered in the next section.Exercises \(144-146\) will help you prepare for the material covered in the next section. Factor the numerator and the denominator. Then simplify by dividing out the common factor in the numerator and the denominator. $$ \frac{x^{2}+6 x+5}{x^{2}-25} $$

Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.
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