36a2 - 60a + 25 = 36a2 - 30a - 30a + 25 = 6a(6a - 5) - 5(6a - 5) = (6a - 5)(6a - 5) = (6a - 5)2
10a-37=6a+51 -6a -6a subtract 6a from both sides and the 6a's cancel 4a-37=51 +37 +37 4a=88 /4 /4 a=22
6a
-6a + 8 = 2 -6a = -6 a = 1
a+6a+a=8a
4y - 4 + 3s + 7 - 6a - 4 = 0 4y + 3s + 7 - 6a - 4 = 4 4y + 3s - 6a - 4 = 4 -7 4y + 3s -6a = 4 - 7 + 4 4y + 3s - 6a = -3 + 4 4y + 3s - 6a = 1 y + 3s - 6a = 1/4 y = -3s + 6a + 1/4 3s = -y + 6a + 1/4 s = -1/3y + 6a + 1/4 -6a = -1/3y + a + 1/4 -a = -1/3y x 1/6 + a + 1/4 x 1/6 a = 1/18y - 1 - 1/24 a = 1/18y - 25/24
Divide by 6a: 6a(a + 3b)
36a2 - 60a + 25 = 36a2 - 30a - 30a + 25 = 6a(6a - 5) - 5(6a - 5) = (6a - 5)(6a - 5) = (6a - 5)2
10a-37=6a+51 -6a -6a subtract 6a from both sides and the 6a's cancel 4a-37=51 +37 +37 4a=88 /4 /4 a=22
6a
18
-6a + 8 = 2 -6a = -6 a = 1
12a2b + 6a = 6a(2ab + 1)
a+6a+a=8a
Using the identity, sin(X)+sin(Y) = 2*sin[(x+y)/2]*cos[(x-y)/2] the expression becomes {2*sin[(23A-7A)/2]*cos[(23A+7A)/2]}/{2*sin[(2A+14A)/2]*cos[(2A-14A)/2]} = {2*sin(8A)*cos(15A)}/{2*sin(8A)*cos(-6A)} = cos(15A)/cos(-6A)} = cos(15A)/cos(6A)} since cos(-x) = cos(x) When A = pi/21, 15A = 15*pi/21 and 6A = 6*pi/21 = pi - 15pi/21 Therefore, cos(6A) = - cos(15A) and hence the expression = -1.
6a2
6a add 21 = 27