Multiplication of polynomials will be done as per the following steps.
- Multiply each term in the first polynomial by each term in another polynomial.
- Combine the like terms and add them.
Here are examples of multiplication of monomials, binomials as well as the polynomials.
Monomial with Monomial [ 1 term * 1 term ]
To multiply one monomial by another monomial, we have to first multiply the constant, then multiply each variable together and then combine the results.
Example: (4xy )(8y)
Solution: (4xy)(8y) = 4.8.xy.y =
Monomial with Binomial [ 1 term * 2 terms]
To multiply one monomial with the binomial term, we have to multiply single term with each of two-term and then combine the results.
Example: 5y( y + 3yz)
Solution: 5y( y + 3yz) = 5y.y + 5y.3yz =
Binomial with Monomial [ 2 terms * 1 term]
To multiply binomial term with monomial, just multiply each term of binomial with the single term and then combine the results.
Example:
Solution:
Binomial with Binomial [ 2 terms * 2 terms]
To multiply two binomial, we have to follow the concept of FOIL (First Outer Inner Last) method and then combine the like terms and add them.
Example: (x+4) (x+8)
- The F stands for first, which means the x in the first factor times the x in the second factor.
- The O stands for outer, which means the x in the first factor times the 8 in the second factor.
- The I stands for inner, which means the 4 in the first factor times the x in the second factor.
- The L stands for last, which means the 4 in the first factor times the 8 in the second factor.
Solution: (x+4) (x+8) =
Binomial with Trinomial [ 2 terms * 3 terms]
Here FOIL doesn’t work, beacuse there are more terms. Following are the steps to multiply a 2 term polynomial with trinomial term.
- Take the first term in polynomial one and multiply it with every term in the second polynomial
- Follow the rule of changing sign while multiplying.
- Take the second term in polynomial one and multiply it with every term in the second polynomial
- Follow the rule of changing sign while multiplying.
- Now combine the like terms to obtain the result.
Example:
Solution:
Exercise
Multiply the following polynomials
