Idea
To multiply a monomial by a polynomial, use the distributive property: multiply the monomial by each term in the polynomial.
Step-by-step method
- Identify the monomial and the polynomial.
- Distribute the monomial to every term inside the parentheses.
- Multiply coefficients and combine variables by adding exponents for like bases.
- Simplify each product.
- Combine like terms if any appear in the result.
Example pattern
If you have something like (a(b+c-d)), rewrite it as:
If variables are involved, remember:
- (x^m \cdot x^n = x^{m+n})
Check your work
Make sure:
- every term in the polynomial was multiplied,
- signs were handled correctly,
- the final expression is fully simplified.
A good check is to look for missing terms or sign mistakes. If the polynomial has three terms, your answer should usually have up to three terms before combining like terms.