The document shows 8 examples of algebraic expressions being simplified through the use of algebraic properties and identities. The expressions are factorized and like terms are combined. Through these steps, the expressions are reduced to their simplest forms in fewer steps.

1. 1.F= X Y Z + XYZ + XYZ + XYZ + XYZ + XYZ
F= X ( Y Z + YZ +YZ) +X( YZ + YZ + YZ)
F= X ( Y( Z + Z) +YZ) +X( Y(Z +Z) + Y Z)
1 1
F= X ( Y + YZ) + X( Y+ Y Z)
F= X ( Y + YZ) + X( Y+ Z)
F= X Y + XZ + XY+X Z
F= X Y + Z( X-X)XY
F= X Y + Z+XY
2- F= ABC+ ABC +ABC+ ABC+ABC + AB C
F= (ABC + A BC ) + ( ABC+ ABC) + ( ABC + AB C)
F=BC(A+A) + AB(C+C)+AB( C+C)
F= BC.1 + AB. 1 + A B .1
F=BC+ (AB + A B )
F= BC + B ( A + A)
FC= BC+ B-1
FC= BC + B
3- F= (A + B) (A+C) C
F= (A + B) (AC +CC)
F= (A+B) (AC+ C)
F= AAC + AC + ABC+ BC
F= 0.C + AC + ABC + BC
F= 0 + (ABC + AC) + BC
F= C (A+ A B) + BC
F= C (A+B) +BC
F= AC + BC + BC
F= AC + BC
F= C (A+B)

2. 4- F= Y (X + Y) ( X + Z )
F= (XY + Y Y) (X + Z )
F= (XY + 0) (X + Z )
F= (XY) (X + Z)
F= X X Y + XYZ
F= 0.Y + XYZ
F= 0 + XYZ
F= XYZ
5- F= X ( X+Y) +Z + ZY
F= ( X X+XY) +Z + ZY
F= ( 0+ X Y+XY) +Z + ZY
F= X Y + Z+ ZY
F=Y(X+ Z)+ Z
6- F= AB + AB + AB +AB
F= ( AB + AB) + (AB + AB)
F= B ( A + A) + B(A + A)
F= B .1 + B.1
F= (B + B)
F=1
7. F= W + X W + YZ
F= W. XW . YZ
F= W. (X + W) . (Y+ Z)
F= W. (X + W) . (Y+ Z)
F= W X + WW (Y + Z)
F= WX + W (Y+ Z)
F= W (X + 1) (Y+Z)

3. F= W . 1 (Y + Z)
F= W (Y + Z)
8 - F= W. [(X+Y) (Z+W)]
F= W+ (X+Y ) (Z+W)
F= W + (X+Y) + (Z+W)
F= W + XY + ZW
F= W+ X+ Y+ Z+ W
F= W + W+ X+ Z+ Y
F= W + X+ Y+ Z