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

Step by step solution

01

Apply distributive property

The distributive property of multiplication over addition allows us to multiply each term of the expression \((8 x^{3} + 3)\) with each term in the expression \((x^{2} - 5)\). Therefore, we have: \[ (8x^{3} * x^{2}) - (8x^{3} * 5) + (3 * x^{2}) - (3 * 5) \].
02

Simplify each term

Now we simplify each term: \[ (8x^{5}) - (40x^{3}) + (3x^{2}) - 15 \].T
03

Combine like terms

Here, there are no like terms to combine, so the final simplified expression is: \[ 8x^{5} - 40x^{3} + 3x^{2} - 15 \]

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Most popular questions from this chapter

a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?

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