Perfect Square Trinomial Example

In algebra, the perfect square trinomial is the result of a binomial squared. When you have a binomial and this multiplies by itself, you get three terms that can no longer be reduced: this is called the perfect square trinomial.

To better understand what a perfect square trinomial is, a squared binomial is developed below:

(a + b)²

The rule for expressing a binomial squared is:

• Square of the first term: (a)² = to²
• Plus the double product of the first by the second: + 2 * (a) * (b) = + 2ab
• Plus the square of the second: + (b)² = + b²

The perfect square trinomial is:

to² + 2ab + b²

It is easy to obtain the original binomial by paying attention to the previous steps, and recognizing each of the terms. In this way it can be said: “to² + 2ab + b² comes from (a + b)²”.

A very different matter occurs with expressions like 3a + 2g - 5x, a trinomial that does not come from a squared binomial. To begin with, nothing squared gives a negative sign, as in the term "-5x”. On the other hand, we have three different variables: to, g, x.

Examples of perfect square trinomial

Perfect square trinomials are listed, from their original squared binomials.

1.- (a + b)² = to² + 2ab + b²

2.- (2a + 2b)² = 4th² + 8ab + 4b²

3.- (a + 2b)² = to² + 4ab + 4b²

4.- (2a + b)² = 4th² + 4ab + b²

5.- (a - b)² = to² - 2ab + b²

6.- (x + y)² = x² + 2xy + y²

7.- (2y - z)² = 4y² - 4yz + z²

8.- (4x + 2a)² = 16x² + 16ax + 4a²

9.- (3f - 5g)² = 9f² - 30fg + 25g²

10.- (f - 4h)² = F² - 8h + 16h²

11.- (2d + 7a)² = 4d² + 28ad + 49a²

12.- (10x + 5y)² = 100x² + 100xy + 25y²

13.- (4a - bc)² = 16th² - 8abc + b²c²

14.- (x² + and²)² = x⁴ + 2x²Y² + and⁴

15.- (to³ + b²)² = to⁶ + 2a³b² + b⁴

16.- (f⁴ - g³)² = F⁸ - 2f⁴g³ + g⁶

17.- (3rd⁵ + x)² = 9a¹⁰ + 6a⁵x + x²

18.- (12d⁴ + 4f³)² = 144d⁸ + 96d⁴F³ + 16f⁶

19.- (4m + n⁷)² = 16m² + 8mn⁷ + n¹⁴

20.- (2nd³ + 2b⁴)² = 4to⁶ + 8a³b⁴ + 4b⁸

• Keep reading: Trinomial squared.