Multiply Monomials

Multiply monomials

When multiplying monomials, combine the numerical parts and the variable parts separately. The goal is to simplify the product completely.

1) Multiply the coefficients

Multiply the numbers in front of the variables. Pay attention to signs:

• positive × positive = positive
• positive × negative = negative
• negative × negative = positive

2) Multiply like bases

For the same variable, add the exponents:

• (x^a \cdot x^b = x^{a+b}) This works for each variable that appears in both monomials.

3) Write the simplified result

Combine everything into one monomial. Put the coefficient first, then the variables in a clear order.

Example

(3x^2 \cdot 4x^5 = 12x^{2+5} = 12x^7)

Check your work

• Did you multiply the coefficients correctly?
• Did you add exponents only for matching variables?
• Did you keep the sign of the product?
• Is the final answer fully simplified?

If a variable appears in only one factor, keep its exponent as is. If there are several variables, simplify each one separately.