Factoring

 

Special products and factoring

a(x+y) = ax+ay

(x+y)(x-y) = x2 - y2

(x+y)2 = x2+2xy+y2

(x-y)2 = x2-2xy+y2

(x+a)(x+b) = x2+(a+b)x+ab

(ax+b)(cx+d)=acx2+(bc+ad)x+bd

(x+y)3 = x3+3x2y+3xy2+y3

(x-y)3 = x3-3x2y+3xy2-y3

(x+y)(x2-xy+y2) = x3+y3

(x-y)(x2+xy+y2) = x3-y3

 

Exercises

Use the special products and factoring equations to solve the following problems by substitution

(2y+2x)3

 

 

(3a+2b)(3a-2b)

 

 

(5w-2v)(25w2+10wv+4v2)

 

 

(3z-4t)3

 

 

3(2a-5b)

 

 

(2x-3)(2x+3)

 

 

(2x-3z)2

 

 

(2a+3b)(4a2-6ab+9b2)

 

 

(3x+2)(4x+3)

 

 

(3x+2y)2

 

 

 

Factoring by Inspection

 

5bx+7by

 

 

25a2-9b2

 

 

16a2+24ab+9b2

 

 

8a3-27b3

 

 

x2-3x-10

 

 

Factoring by Grouping

cx-2cy-6dy+3dx

 

 

4a2-9x2-6x-1

 

 

9x2-6xy+y2-25a2+10ab-b2

 

 

(y2+y-9)2-9