2. Formula method

Square difference: a 2-b 2 = (a-b) (a+b)

For example: 25x 2-49 = (5x) 2-7 2 = (5x-7) (5x+7)

a^4-9a^2b^2=a^2(a^2-9b^2)=a^2(a-3b)(a+3b)

Complete square: (a b) 2 = a 2 2ab+b 2.

For example: 9x2-66x+121= (3x) 2-2 * 3 *1112 = (3x-1655.

9x^2-30x+25 =(3x-5)^2

( 1)a^3+b^3=(a+b)(a^2-ab+b^2)

(2)a^3-b^3=(a-b)(a^2+ab+b^2)

Example: a 3+b 3+c 3-3 ABC- add 3a 2 * b+3a * b 2 to make (a+b) 3, and then subtract it.

= (a3+3a2 * b+3a * B2+B3)+C3-3a2 * b-3a * B2-3abc-(addition is used here)

=[(a+b)3+C3]-3ab(a+b+c)- gives the common factor of the last three terms.

= (a+b+c) [(a+b) 2-(a+b) c+c 2)-3ab (a+b+c)-Apply the above formula to (A+B) 3+C 3.

=(a+b+c)[(a+b)2-(a+b)c+C2-3ab]-

=(a+b+c) [a^2+b^2+c^2-ab-ab-bc]

(3)x2+(a+b)x+ab =(x+a)(x+b)- also belongs to the cross method.

3, cross method:

(ax+p)(bx+q)=abx^2+(aq+bp)x+pq

Example: A 2-A-6 =(A-3)(A+2)- decompose -6 into -3*2, and at the same time -3+2=- 1 (linear coefficient).

X2-9x+ 18 =(x-3)(x-6)- Divide 18 into -3 *(6) and -3+(-6)=-9 (linear coefficient).

4. Grouping decomposition method

Example: 5ax+5bx+3ay+3by = 5x (a+b)+3y (a+b)-Put 5ax and 5bx, 3ay and 3by together.

=(5x+3y)(a+b)

5. Add items and delete items-Add items as described above.

Example: x 3-1 1x+20- (decomposition: decompose-1 1x into-16x+5x) and then decompose in groups.

=(x^3- 16x)+(5x+20)

= x (x 2-16)+5 (x+4)-square difference

=x(x+4)(x-4)+5(x+4)

=(x+4)(x^2-4x+5)