# How to Recognize a Perfectly Squared Binomial

Recognizing a perfectly squared binomial can make life easier. When you recognize a perfectly squared binomial, you’ve identified a shortcut that saves time when distributing binomials over other terms.

When the same binomial is multiplied by itself — when each of the first two terms is distributed over the second and same terms — the resulting trinomial contains the squares of the two terms and twice their product. For example,

** Example 1: **You can see with the following binomial that the same binomial is being multiplied by itself. So, the result of the distribution is the sum of the squares of

*x*

*and 3 along with twice their product.*

*Example 2*** : **Try the binomial distribution, (4

*y*– 5)(4

*y*– 5), which contains negative signs.

The square of –5 is +25. (Note that the square is positive.)

Twice the product of 4*y* and –5 is 2(4*y*)(–5) = –40*y*

*Example 3*** : **Use the shortcut for the expression,

where the terms are all variables.

*Example 4*** : **You can use the shortcut even with the expression, [

*x*+ (

*a*+

*b*)][

*x*+ (

*a*+

*b*)], where parentheses group the last two terms together in this distribution.