Question

Ab-a-b+1

I know it splits into a(b-1)-1(b-1) but can someone explain in words how it becomes (a-1)(b-1) thanks

Answer 1

ab - a - b + 1 = (a - 1)(b - 1)

Explanation:

Let us explain factorization by grouping

In the expression of 4 terms ax + by + bx + ay

Take every two terms have a common factor in a bracket

• (ax + ay) + (bx + by)

Take the common factor out of the brackets

• a(x + y) + b(x + y)

Take the bracket as a common factor

• (x + y)(a + b)

Let us do these steps with our question

∵ ab - a - b + 1 is an expression of 4 terms

→ Take ab and a in a bracket, -b and 1 in another bracket

∴ ab - a - b + 1 = (ab - a) + (-b + 1)

→ Take a as a common factor from the 1st bracket and -1 from

the 2nd bracket

∴ (ab - a) + (-b + 1) = a(b -1) + -1(b - 1)

→ Take the bracket (b - 1) as a common factor

∴ a(b -1) + -1(b - 1) = (b - 1)(a + -1)

∵ (+)(-) = (-)

∴ (b - 1)(a + -1) = (b - 1)(a -1)

→ Change the order of the bracket

∴ (b - 1)(a -1) = (a - 1)(b - 1)

∴ ab - a - b + 1 = (a - 1)(b - 1)