Question

\\3x(4x^2 + x - 3y + 2)\\

Explanation:

Identify the expression

We are given an algebraic expression involving a monomial multiplied by a polynomial:

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

Apply the distributive property

Using the Distributive Property knowledge point

$$
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$$

Multiply the individual terms

We multiply the coefficients and add the exponents of like variables:

• First term: \(3x \cdot 4x^2 = 12x^3\)
• Second term: \(3x \cdot x = 3x^2\)
• Third term: \(-3x \cdot 3y = -9xy\)
• Fourth term: \(3x \cdot 2 = 6x\)

Combining these terms gives:

$$ 12x^3 + 3x^2 - 9xy + 6x $$

Answer:

\(12x^3 + 3x^2 - 9xy + 6x\)