Let's simplify the given expression step by step:

Expression:

$3x(4x - 6y^2) + 6x(3y^2 - 2x)$

Step 1: Expand each term

Expand $3x(4x - 6y^2)$: $3x(4x - 6y^2) = 12x^2 - 18xy^2$

Expand $6x(3y^2 - 2x)$: $6x(3y^2 - 2x) = 18xy^2 - 12x^2$

Step 2: Combine the expanded terms

Now combine: $12x^2 - 18xy^2 + 18xy^2 - 12x^2$

Step 3: Simplify by combining like terms

• $12x^2 - 12x^2 = 0$
• $-18xy^2 + 18xy^2 = 0$

Final Simplified Result:

$\boxed{0}$

The entire expression simplifies to $0$.

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Would you like further clarification on this or examples of similar problems?

Here are 5 related questions for practice:

1. Simplify $2x(3x - 4y) + 4x(2y - 3x)$.
2. Expand and simplify $5x(4x + 6y) + 2y(3x - 2y)$.
3. Solve $6x(2x - y) - 3x(4x - 2y)$.
4. Factorize $12x^2 - 18xy^2 + 18xy^2 - 12x^2$.
5. What happens if we introduce additional terms, like $+2y^2$, to the original expression?

Tip:

Always double-check your expansion and simplify terms systematically to avoid mistakes.