Transcript Polynomial and Multiplication of

Polynomial and Multiplication of
1 or more terms separated by
addition or subtraction
• Term – number, variable or combination of
both 2, y, 3x
• Degree – highest exponent in the polynomial
• How to write a polynomial – put in order of
highest exponent on variable to the lowest
• Monomial – 1 term
• Binomial – 2 terms
• Trinomial – 3 terms
Multiplying Polynomials
• Monomial times Monomial
– Multiply the coefficients together
– Multiply the variables together
• If the variables are different just write them next to
each other
• If the variables are the same add the exponents
Monomial times binomial
• Distribute the term outside the ( ) to all the terms
inside
Binomial times Binomial
• This is still distribution, but we follow the FOIL method
which just helps us to remember to multiply all terms
in first binomial to all terms in the second binomial
• FOIL
– (F)irst – multiply the first term in each binomial
– (O)utside – multiply the first term in the first binomial and
the last term in the second binomial
– (I)nside – multiply the second term in the first binomial to
the first term in the second
– (L)ast – multiply the last terms in each of the binomials
– A lot of the time you can combine like terms look for this
Polynomial times Polynomial
• Make sure all the terms in the first polynomial
are distributed to all the terms in the second
polynomials
• 4 term poly times another 4 term poly will
give you 16 terms, but some may be
combined
Special Cases
Perfect Square – if a binomial is being squared
you are multiplying it by itself
( x  2)  ( x  2)( x  2)
2
Sum and difference – same terms in each
binomial but the signs are opposite, one is
addition and one is subtraction
( x  3)( x  3)
Perfect Square
(a  b)  a  2ab  b
2
(a  b)  a  2ab  b
2
2
2
2
2
Sum and Difference
(a  b)(a  b)  a  b
2
2