To multiply two polynomials, you apply the distributive property. Consider a simple example: multiplying a monomial 3x by the binomial x - 2.
When you multiply one binomial by another binomial, you have to use the distributive property repeatedly.
There's a shortcut you can use here, known as the "FOIL" method (that stands for First, Outer, Inner, Last.). The product of two binomials is the sum of four simpler products.
The product of the First terms is: (x)(x) = x2
The product of the Outer terms is: (x)(–7) = –7x
The product of the Inner terms is: (2)(x) = 2x
And the product of the Last terms is: (2)(–7) = –14
Add all these up, and you'll get the answer:
(x + 2)(x – 7) = x2 + (–7x) + 2x + (–14)
= x2 – 5x – 14
You can use a similar strategy to multiply trinomials or other polynomials. For example, to multiply:
you need to find six products:
and then add them all up to get .