Products and Factors
5-6Squares of Binomials
Overview
(a + b)^2 = a^2 + 2ab + b^2; (a − b)^2 = a^2 − 2ab + b^2.
Key ideas
- Square the first term, twice the product, square the last.
- Used in completing the square later.
- Recognize ‘perfect-square trinomials.’
Worked examples
Example 1
Problem. (x + 4)^2
Solution. x^2 + 8x + 16
Example 2
Problem. (2y − 3)^2
Solution. 4y^2 − 12y + 9
Practice
Try each one. Click Show answer when ready.
- 1.
(x + 6)^2
- 2.
(y − 5)^2
- 3.
(3a + 2)^2
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Expand: (3x − 5y)².
- 2.
Expand: (2a + 3b)².