Factor each completely.
Problem 1 :
16n2 - 9
Solution :
16n2 - 9
= (42n2 - 32)
= ((4n)2 - 32)
(a2 - b2) = (a + b) (a - b)
= (4n + 3) (4n - 3)
Problem 2 :
4m2 - 25
Solution :
= 4m2 - 25
= (22m2 - 52)
= ((2m)2 - 52)
(a2 - b2) = (a + b) (a - b)
= (2m + 5) (2m - 5)
Problem 3 :
16b2 - 40b + 25
Solution :
= 16b2 - 40b + 25
= 16b2 - 20b - 20b + 25
= 4b(4b - 5) - 5(4b - 5)
= (4b - 5) (4b - 5)
= (4b - 5)2
Problem 4 :
4x2 - 4x + 1
Solution :
= 4x2 - 4x + 1
= 4x2 - 2x - 2x + 1
= 2x(2x - 1) - 1(2x - 1)
= (2x - 1) (2x - 1)
= (2x - 1)2
Problem 5 :
9x2 - 1
Solution :
= 9x2 - 1
= (32x2 - 12)
= ((3x)2 - 12)
(a2 - b2) = (a + b) (a - b)
= (3x + 1) (3x - 1)
Problem 6 :
n2 - 25
Solution :
= n2 - 25
= (n2 - 52)
(a2 - b2) = (a + b) (a - b)
= (n + 5) (n - 5)
Problem 7 :
n4 - 100
Solution :
= n4 - 100
= ((n2)2 - 102)
(a2 - b2) = (a + b) (a - b)
(n2 + 10) (n2 - 10)
Problem 8:
a4 - 9
Solution :
= a4 - 9
= ((a2)2 - 32)
(a2 - b2) = (a + b) (a - b)
= (a2 + 3) (a2 - 3)
Problem 9 :
k4 - 36
Solution :
= k4 - 36
= ((k2)2 - 62)
(a2 - b2) = (a + b) (a - b)
= (k2 + 6) (k2 - 6)
Problem 10 :
n4 - 49
Solution :
= n4 - 49
= ((n2)2 - 72)
(a2 - b2) = (a + b) (a - b)
(n2 + 7) (n2 - 7)
Problem 11 :
98n2 - 200
Solution :
= 98n2 - 200
= 2(49n2 - 100)
= 2(72n2-102)
= 2((7n)2 - 102)
(a2 - b2) = (a + b) (a - b)
= 2(7n + 10) (7n - 10)
Problem 12 :
3 + 6b + 3b2
Solution :
= 3b2 + 6b + 3
= 3(b2 + 2b + 1)
= 3(b + 1)2
Problem 13 :
400 - 36v2
Solution :
= 400 - 36v2
= 4(100 - 9v2)
= 4(102 - 32v2)
= 4(102 - (3v)2)
(a2 - b2) = (a + b) (a - b)
4(10 + 3v) (10 - 3v)
Problem 14 :
100x2 + 180x + 81
Solution :
100x2 + 180x + 81
100x2 + 90x + 90x + 81
10x(10x + 9) + 9(10x + 9)
(10x + 9) (10x + 9)
(10x + 9)2
Problem 15 :
10n2 + 100n + 250
Solution :
10n2 + 100n + 250
10(n2 + 10n + 25)
10(n2 + 5n + 5n + 25)
10n(n + 5) + 5(n + 5)
10(n + 5) (n + 5)
10(n + 5)2
Problem 16 :
49n2 - 56n + 16
Solution :
49n2 - 56n + 16
49n2 - 28n - 28n + 16
7n(7n - 4) - 4(7n - 4)
(7n - 4) (7n - 4)
(7n - 4)2
Problem 17 :
49x2 - 100
Solution :
49x2 - 100
(72x2 - 102)
((7x)2 - 102)
(a2 - b2) = (a + b) (a - b)
(7x + 10) (7x - 10)
Problem 18 :
1 - r2
Solution :
1 - r2
12 - r2
(a2 - b2) = (a + b) (a - b)
(1 + r) (1 - r)
Problem 19 :
10p3 - 1960p
Solution :
10p3 - 1960p
10p(p2 - 196)
10p(p2 - 142)
(a2 - b2) = (a + b) (a - b)
10p(p + 14) (p - 14)
Problem 20 :
343b2 - 7b4
Solution :
343b2 - 7b4
7b2(49 - b2)
7b2(72 - b2)
(a2 - b2) = (a + b) (a - b)
7b2(7 + b) (7 - b)
Problem 21 :
81v4 - 900v2
Solution :
81v4 - 900v2
9v2(9v2 - 100)
9v2(32v2-102)
9v2((3v)2 - 102)
(a2 - b2) = (a + b) (a - b)
9v2(3v + 10) (3v - 10)
Problem 22 :
200m4 + 80m3 + 8m2
Solution :
200m4 + 80m3 + 8m2
8m2(25m2 + 10m + 1)
8m2(25m2 + 5m + 5m + 1)
8m2 5m(5m + 1) + 1(5m + 1)
8m2 (5m + 1) (5m + 1)
8m2 (5m + 1)2
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM