Square of a Binomial
The square of a binomial is
always
a trinomial. It will be helpful to memorize these patterns for writing squares of binomials as trinomials.
Examples:
Square each binomial.
If the coefficients of a
trinomial
satisfy the equation
,
then the trinomial is the
perfect square
of the
binomial
.
Example 1:
Factor, if possible.
Here,
. We have:
So, the trinomial is a perfect square:
You can verify this using
FOIL
.
Example 2:
Factor, if possible.
Here,
. (We can treat
as
, and not worry about the fourth power.)
So, the trinomial is a perfect square:
This can also be verified using FOIL.