Question

ab+ac

ab-ac+ad

ax-bx-cx-dx

a(b+c)-d(b+c)

ac-ad+bc-bd

ax+by+bx+ay

Answer 1

a) \(ab+ac=a.\left(b+c\right)\)

b) \(ab-ac+ad=a.\left(b-c+d\right)\)

c) \(ax-bx-cx-dx=x.\left(a-b-c-d\right)\)

d) \(a.\left(b+c\right)-d.\left(b+c\right)=ab+ac-db-dc=b.\left(a-d\right)+c.\left(a-d\right)=\left(a-d\right).\left(b+c\right)\)

e) \(ac-ad+bc-bd=a.\left(c-d\right)+b.\left(c-d\right)=\left(c-d\right).\left(a+b\right)\)

f) \(ax+by+bx+ay=a.\left(x+y\right)+b.\left(y+x\right)=\left(x+y\right).\left(a+b\right)\)

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