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Special Products of Polynomials
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Perfect-Square Trinomial
A perfect-square trinomial is a trinomial that is the result of squaring a binomial.
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Example 1 (x + 3)2 (x + 3)2 = (x + 3)(x + 3) = x2 + 3x + 3x + 9
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Short Cut Square the first term
Multiply the two terms together and double the result. Square the last term.
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Example 2 (5a + b)2 (a + b)2 = a2 + 2ab + b2
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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.
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Example 3 (x + 4)(x – 4) (a + b)(a – b) = a2 – b2
(x + 4)(x – 4) = x2 – 42 = x2 – 16
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Example 4 (p2 + 8q)(p2 – 8q) (a + b)(a – b) = a2 – b2
(p2 + 8q)(p2 – 8q) = p4 – (8q)2 = p4 – 64q2
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Example 5 Write an expression that represents the area of the swimming pool.
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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
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Write a polynomial that represents the area of the yard around the pool shown below.
10x + 29
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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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