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Special Products of Polynomials

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Presentation on theme: "Special Products of Polynomials"— Presentation transcript:

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


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