We decompose the following formulas: (1) 18a3bc-45a2b2c2; (2) - 20a-15ab; (3) 18xn + 1-24xn; (4) (M + n) (X-Y) - (M + n) (x + y); (5) 15 (a + b) 2 + 3Y (B + a); (6) 2A (B-C) + 3 (C-B)

We decompose the following formulas: (1) 18a3bc-45a2b2c2; (2) - 20a-15ab; (3) 18xn + 1-24xn; (4) (M + n) (X-Y) - (M + n) (x + y); (5) 15 (a + b) 2 + 3Y (B + a); (6) 2A (B-C) + 3 (C-B)

（1）18a3bc-45a2b2c2=9a2bc（2a-5bc）；（2）-20a-15ab=-5a（4+3b）；（3）18xn+1-24xn=6xn（3x-4）；（4）（m+n）（x-y）-（m+n）（x+y）=（m+n）（x-y-x-y）=-2y（m+n）；（5）15（a+b）2+3y（b+a）=3（a+b）[5（a+b）+y]=3（a+b）（5a+5b+y）；（6）2a（b-c）+3（c-b）=（2a-3）（b-c）．

Using the unit circle, find the set of angles suitable for the following conditions
（1）cos α = - （√2）/2
（2）sin α ≤ 1/2

Factorization of 15 (a-b) ^ 2-3y (B-A)~

Use the unit circle to find the angle 0 '- 360' suitable for the following conditions
Sina greater than or equal to 1 / 2
Tana > root 3

Sina greater than or equal to 1 / 2
A∈[60°,120°]
Tana > root of 3 a ∈ [30 ° 90 °] ∪ [210 ° 270 °]

Factorization of 15 (a-b) ^ 2-3y (B-A)~

5（a-b）^2-3y(b-a)
=5（a-b）^2+3y(a-b)
=（a-b）(5a-5b+3y)

Using the unit circle to write the set of angles satisfying the condition sin α > - 1 / 2

Draw a circle, I and II quadrants satisfy ~ find out the two corners with sin a = - 0.5. The part between the two corners is less than - 0.5

Factorization (a + b) ^ 2 + 2 (a + b) (a-b) - 15 (a-b) ^ 2

Use the unit circle to write the set of angles satisfying Tan x > 1!

First, draw the image of y = TaNx, and then from the topic meaning, TaNx > 1, π / 4 + K π

Please factorize (B & sup2; + C & sup2; - A & sup2;) & sup2;

(B & sup2; + C & sup2; - A & sup2;) & sup2; - 4B & sup2; C & sup2; = (B & sup2; + C & sup2; - A & sup2; + 2BC) (B & sup2; + C & sup2; - A & sup2; - 2BC) = [(B + C) & sup2; - A & sup2;] [(B-C) & sup2; - A & sup2;] = (B + C + a) (B + C-A) (B-C + a) (b-c-a)

It is known that SiNx is equal to half. When x belongs to a real number, the set of values of X

sinx=1/2
When x ∈ [0,2 π],
X = π / 6, or x = 5 π / 6
When x ∈ R,
X = π / 6 + 2K π, or x = 5 π / 6 + 2K π, K ∈ Z
Value set of X
{x | x = π / 6 + 2K π, or x = 5 π / 6 + 2K π, K ∈ Z}