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,
![image0.png](https://www.dummies.com/wp-content/uploads/167676.image0.png)
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.
![image1.png](https://www.dummies.com/wp-content/uploads/167677.image1.png)
![image2.png](https://www.dummies.com/wp-content/uploads/167678.image2.png)
Example 2: Try the binomial distribution, (4y – 5)(4y – 5), which contains negative signs.
![image3.png](https://www.dummies.com/wp-content/uploads/167679.image3.png)
The square of –5 is +25. (Note that the square is positive.)
Twice the product of 4y and –5 is 2(4y)(–5) = –40y
![image4.png](https://www.dummies.com/wp-content/uploads/167680.image4.png)
Example 3: Use the shortcut for the expression,
![image5.png](https://www.dummies.com/wp-content/uploads/167681.image5.png)
where the terms are all variables.
![image6.png](https://www.dummies.com/wp-content/uploads/167682.image6.png)
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.
![image7.png](https://www.dummies.com/wp-content/uploads/167683.image7.png)