Question
Multiply: 1. \( \left(3 x^{3}-2 x\right)\left(2 x^{2}-x-4\right) \)
Ask by Bernard Bryant. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The product is \( 6x^{5}-3x^{4}-16x^{3}+2x^{2}+8x \).
Solution
Calculate or simplify the expression \( (3x^3-2x)(2x^2-x-4) \).
Calculate or simplify the expression \( (3x^3-2x)(2x^2-x-4) \).
Simplify the expression by following steps:
- step0: Multiply the terms:
\(\left(3x^{3}-2x\right)\left(2x^{2}-x-4\right)\)
- step1: Apply the distributive property:
\(3x^{3}\times 2x^{2}-3x^{3}\times x-3x^{3}\times 4-2x\times 2x^{2}-\left(-2x\times x\right)-\left(-2x\times 4\right)\)
- step2: Multiply the terms:
\(6x^{5}-3x^{4}-12x^{3}-4x^{3}-\left(-2x^{2}\right)-\left(-8x\right)\)
- step3: Remove the parentheses:
\(6x^{5}-3x^{4}-12x^{3}-4x^{3}+2x^{2}+8x\)
- step4: Subtract the terms:
\(6x^{5}-3x^{4}-16x^{3}+2x^{2}+8x\)
The product of \( (3x^{3}-2x) \) and \( (2x^{2}-x-4) \) is \( 6x^{5}-3x^{4}-16x^{3}+2x^{2}+8x \).
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Simplify this solution The Deep Dive
To multiply the expressions \( \left(3 x^{3}-2 x\right)\left(2 x^{2}-x-4\right) \), you will need to distribute each term from the first expression with each term from the second. Start by multiplying \( 3x^3 \) by each term in \( 2x^2 - x - 4 \): \[ 3x^3 \cdot 2x^2 = 6x^5 \] \[ 3x^3 \cdot (-x) = -3x^4 \] \[ 3x^3 \cdot (-4) = -12x^3 \] Now, do the same for \( -2x \): \[ -2x \cdot 2x^2 = -4x^3 \] \[ -2x \cdot (-x) = 2x^2 \] \[ -2x \cdot (-4) = 8x \] Now combine all these results: \[ 6x^5 - 3x^4 - 12x^3 - 4x^3 + 2x^2 + 8x \] Combine like terms: \[ 6x^5 - 3x^4 - 16x^3 + 2x^2 + 8x \] So, the final result is: \[ \boxed{6x^5 - 3x^4 - 16x^3 + 2x^2 + 8x} \]
