To multiply a polynomial by a monomial use the Distributive Property.
To multiply two binomials use the FOIL method.
F the product of the first two terms
O the product of the outside terms
I the product of the inside terms
L the product of the last terms
F--- ac
O--- ad
I--- bc
L--- bd
Thus,
Then, combine like terms (if possible).
To multiply a polynomial by another polynomial multiply the second polynomial by each term in the first polynomial, then use the Distributive Property. Finally, combine like terms (if possible).
a( d + e + f ) + b( d + e + f ) + c( d + e + f )=
ad + ae + af + bd + be + bf + cd + ce + cf
Thus,
The following polynomials are very common in algebra. Learning to recognize their forms and solutions would be very beneficial.