Question
What is the product? \( \left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right) ? \) \( 12 x^{9}+15 x^{8}-8 x^{6}-10 x^{5} \) \( 12 x^{24}+15 x^{12}-8 x^{8}-10 x^{4} \) \( 12 x^{9}-10 x^{5} \) \( 12 x^{24}-10 x^{4} \)
Ask by Love Klein. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product is \( 12x^{9} + 15x^{8} - 8x^{6} - 10x^{5} \).
Solution
To find the product, follow these steps:
1. Multiply the first two factors:
x⁴ · (3x³ - 2) = 3x⁷ - 2x⁴
2. Now multiply this result by the third factor (4x² + 5x):
(3x⁷ - 2x⁴) · (4x² + 5x)
Distribute each term:
– 3x⁷ · 4x² = 12x⁹
– 3x⁷ · 5x = 15x⁸
– (-2x⁴) · 4x² = -8x⁶
– (-2x⁴) · 5x = -10x⁵
3. Combine all the terms:
12x⁹ + 15x⁸ - 8x⁶ - 10x⁵
Thus, the correct product is:
12x⁹ + 15x⁸ - 8x⁶ - 10x⁵
The answer is the first option.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the product of \( \left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right) \), you can distribute step-by-step. Start by multiplying \( x^{4} \) with each term inside the parentheses of \( (3 x^{3}-2) \) and \( (4 x^{2}+5 x) \). After computing, collect like terms to simplify your expression. Upon carrying out the multiplication correctly, you will arrive at \( 12 x^{9}+15 x^{8}-8 x^{6}-10 x^{5} \). The key part here is to be systematic in distributing each term to avoid missing any products, as they contribute to the final polynomial!
