Simplify: 3x(2x2+5x−4)3𝑥(2𝑥2+5𝑥−4)

A. 4x2−2x+104𝑥2−2𝑥+10

B. 6x3−5x2+12x6𝑥3−5𝑥2+12𝑥

C. 6x3+15x2−12x6𝑥3+15𝑥2−12𝑥

D. 32x3+10x2−12x


To simplify the expression \(3x(2x^2 + 5x - 4)\), we need to distribute \(3x\) across each term inside the parentheses.

Let's start with the given expression:

\[3x(2x^2 + 5x - 4)\]

We distribute \(3x\) to each term inside the parentheses:

1. Multiply \(3x\) by \(2x^2\):
\[3x \cdot 2x^2 = 6x^3\]

2. Multiply \(3x\) by \(5x\):
\[3x \cdot 5x = 15x^2\]

3. Multiply \(3x\) by \(-4\):
\[3x \cdot (-4) = -12x\]

Now, we combine these results:

\[6x^3 + 15x^2 - 12x\]

So the simplified expression is:

\[6x^3 + 15x^2 - 12x\]

Looking at the answer choices:

A. \(4x^2 - 2x + 10\)
B. \(6x^3 - 5x^2 + 12x\)
C. \(6x^3 + 15x^2 - 12x\)
D. \(32x^3 + 10x^2 - 12x\)

The correct answer is:

C. \(6x^3 + 15x^2 - 12x\)

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you distribute a monomial across a polynomial?
2. What are the steps to simplify polynomial expressions?
3. How would you factorize the expression \(6x^3 + 15x^2 - 12x\)?
4. What is the difference between distribution and factoring in algebra?
5. How do you handle expressions with higher degree polynomials in distribution?

**Tip:** Always check each term after distribution to ensure accuracy in simplification.

Learn how to simplify the expression 3x(2x^2 + 5x - 4) step-by-step with detailed explanations. This problem involves distributing a monomial across a polynomial and simplifying the resulting polynomial expression. Suitable for Grades 7-9.

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