The document discusses how to find the square of a binomial expression using the formula F2 + 2FL + L2, where F is the first term, L is the last term, and examples are provided to demonstrate its use. The key steps are: (1) square the first term for F2, (2) multiply the first and last terms and double the product for 2FL, and (3) square the last term for L2. Several examples of finding the square of binomial expressions such as (x + 2)2, (x - 3)2, and (3 - 6x)2 are worked through to illustrate the application of the formula.

1. by. G. Martin

2. The square of a binomial is always a trinomial and the result is a
Perfect Square Trinomial.
To solve for the square of trinomial, use the formula of:
F2 + 2FL + L2.
where,
1st term ( F2 ) = Square the first term of the binomial.
2nd term (2FL ) = Twice the product of the first term and the second
term of the binomial.
3rd term (L2 ) = Square of the second term / last term of the binomial

3. Example 1. Find the product of (x + 2)2
Solution:
(x + 2)2 means (x + 2) (x + 2)
F2 (square the first term) = (x)2 = x . X = x2
2FL ( twice the product of the first and second / last term) = 2(x
. 2) = 2(2x) = 4x
L2 ( square the last term)= (2)2 = 2 . 2 = 4
= x2 + 4x + 4

4. Example 2. Find the product of (x -3)2
Solution:
(x – 3)2 means (x - 3) (x – 3)
F2 = (x)2 = x . x = x2
2FL = 2(x . -3) = 2(-3x) = -6x
L2 = (-3)2 = -3 . -3 = 9
= x2 – 6x + 9

5. Example 3. Find the product of (m + 4)2
Solution:
F2 = (m)2 = m . m = m2
2FL = 2(m . 4) = 2(4m) = 8m
L2 = (4)2 = 4 . 4 = 16
= m2 + 8m + 16

6. Example 4. Find the product of (2x + 5)2 .
Solution:
F2 = (2x)2 = 2x . 2x = 4x2
2FL = 2(2x . 5) = 2(10x) = 20x
L2 = (5)2 = 5. 5 = 25
= 4x2 + 20x + 25

7. Example 5. Find the product of (x3 – 2y)2
Solution:
F2 = (x3)2 = x3 . x3 = x6
2FL = 2(x3 . -2y) = 2(-2x3y) = -4x3y
L2 = (-2y)2 = (-2y . -2y) = 4y2
= x6 – 4x3y + 4y2

8. Example 6. Find the product of (3 – 6x)2
Soulution:
F2 = (3)2 = 3. 3 = 9
2FL = 2(3 . -6x) = 2(-18x) = -36x
L2 = (-6x)2 = -6x . -6x = 36x2
= 9 – 36x + 36x2
Arrange in standard form = 36x2 – 36x + 9

9. THANK YOU!