Factor Special Products April 4, 2014 Pages 600-602.
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Factor Special Factor Special Products Products April 4, 2014 Pages 600-602
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Transcript of Factor Special Products April 4, 2014 Pages 600-602.
Factor Special Factor Special ProductsProducts
April 4, 2014
Pages 600-602
Factor the polynomial.
1. y2 – 16
= (y + 4)(y – 4)
2. 25m2 – 36
= (5m + 6)(5m – 6)
3. x2 – 49y2
= (x + 7y)(x – 7y)
Write as a2 – b2.
Difference of two squares pattern
Write as a2 – b2.
Difference of two squares pattern
Write as a2 – b2.
Difference of two squares pattern
= y2 – 42
= (5m)2 – 62
= x2 – (7y)2
4. 8 – 18n2
= 2(4 – 9n2)
= 2[22 – (3n) 2]
= 2(2 + 3n)(2 – 3n)
Factor out common factor.
Write 4 – 9n2 as a2 – b2.
Difference of two squares pattern
5. 4y2 – 64
= (2y + 8)(2y – 8)
Write as a2 – b2.
Difference of two squares pattern
= (2y)2 – (8)2
Perfect Square Trinomial Pattern
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
6.
n2 – 12n + 36 = n2 – 2(n 6) + 62 Write as a2 – 2ab + b2.
= (n – 6)2 Perfect square trinomial pattern
7. 9x2 – 12x + 4 Write as a2 – 2ab + b2.
= (3x – 2)2 Perfect square trinomial pattern
8. 4s2 + 4st + t2 = (2s)2 + 2(2s t) + t2 Write as a2 + 2ab + b2.
= (3x)2 – 2(3x 2) + 22
= (2s + t)2 Perfect square trinomial pattern
Factor the polynomial.
9. – 3y2 + 36y – 108.
– 3y2 + 36y – 108 Factor out – 3.
= – 3(y2 – 2(y 6) + 62) Write y2 – 12y + 36 as a2 – 2ab + b2.
= – 3(y – 6)2 Perfect square trinomial pattern
= – 3(y2 – 12y + 36)
= (h + 2)2 Perfect square trinomial pattern
Write as a2 +2ab+ b2.10. h2 + 4h + 4
11. 2y2 – 20y + 50
Write as y2 –10y+25 as a2 –2ab+b2 .
Factor out 2
= 2(y – 5)2 Perfect square trinomial pattern
= 2[y2 –2(y 5) + 52]
= h2+2(h 2) +22
= 2(y2 – 10y +25)
12. Solve the equation x2 + + = 0.23
x 19
9x2 + 6x + 1 = 0 Multiply each side by 9 to get rid of the fractions.
(3x)2 + 2(3x 1) + (1)2 = 0 Write left side as a2 + 2ab + b2.
(3x + 1)2 = 0 Zero- product property
x = – 13
Solve for x.
ANSWER
The solution of the equation is – .13
a2 + 2(a 3) +(3)2 = 0 Write left side as a2 + 2ab + b2.
(a + 3)2 = 0 Zero-product property
Solve for a.
Solve the equation
13. a2 + 6a + 9 = 0
a = – 3
a + 3 = 0 Perfect square trinomial pattern
w2 + 2(w 7) +(7)2 = 0 Write left side as a2 – 2ab + b2.
(w – 7)2 = 0 Zero-product property
Solve for w.
14. w2 – 14w + 49 = 0
w = 7
w – 7 = 0 Perfect square trinomial pattern
Write left side as a2 – 2ab + b2.
(n + 9) (n – 9) = 0
Zero-product property
Solve for w.
15. n2 – 81= 0
n2 – 92 = 0
(n + 9) = 0 (n – 9) = 0or
n = – 9 or n = 9
Difference of two squares pattern
HOMEWORKHOMEWORK
Worksheet
