1Cademy - Multiplying $$(3x^2)(-4x^3)$$

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Monomial

Example

Multiplying $(3x^2)(-4x^3)$

Multiply the two single-variable monomials $(3x^2)(-4x^3)$ .

Step 1 — Rearrange using the Commutative Property. Group the numerical coefficients together and the powers of $x$ together:

$3 \cdot (-4) \cdot x^2 \cdot x^3$

Step 2 — Multiply the coefficients and apply the Product Property. The coefficients have different signs, so their product is negative: $3 \cdot (-4) = -12$ . For the variable part, both factors share the base $x$ , so add the exponents: $x^2 \cdot x^3 = x^{2+3} = x^5$ .

The result is $-12x^5$ .

This example demonstrates the basic pattern for multiplying two monomials that share a single variable: rearrange to separate the numerical and variable parts, multiply the numbers, and add the exponents on the common base.

Updated 2026-04-29

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