1. Special Products of Polynomials

2. Perfect-Square Trinomial
A perfect-square trinomial is a trinomial that is the result of squaring a binomial.

3. Example 1 (x + 3)2 (x + 3)2 = (x + 3)(x + 3) = x2 + 3x + 3x + 9

4. Short Cut Square the first term
Multiply the two terms together and double the result.
Square the last term.

5. Example 2 (5a + b)2 (a + b)2 = a2 + 2ab + b2

6. Difference of Two Squares
If your two binomials have the same numbers, but one is adding them and the other is subtracting them:
Square the first term.
Square the last term.
Write them as a difference.

7. Example 3 (x + 4)(x – 4) (a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 42
= x2 – 16

8. Example 4 (p2 + 8q)(p2 – 8q) (a + b)(a – b) = a2 – b2
(p2 + 8q)(p2 – 8q) = p4 – (8q)2
= p4 – 64q2

9. Example 5
Write an expression that represents the area of the swimming pool.

10. Try these… (x + 8)(x – 8) X2 - 64 (x + 6)2 X2 + 12x + 36 (4m – 10)2
16m2 -80m + 100
(3 + 2y2)(3 – 2y2)
-4y2 + 9
(5a + 2b)2
25a2 + 20ab + 4b2
(7 – r3)2
r6 -14r3 + 49

11. Write a polynomial that represents the area of the yard around the pool shown below.
10x + 29

12. Write a polynomial that represents the shaded area of the figure below.
x + 6
x – 7
x – 6
x – 7
14x - 85