Question

Factorise : a(a-1)-b(b-1)

Answer 1

$\textbf{Given:}\\\\a(a-1)-b(b-1)\\\\\textbf{To find:}\\\\\text{Factors of a(a-1)-b(b-1) }\\\\\textbf{Solution:}\\\\\text{Consider,}\\\\a(a-1)-b(b-1)\\\\=a^2-a-b^2+b\\\\=a^2-b^2-a+b\\\\=(a^2-b^2)-(a-b)\\\\\text{Using the identity,}\\\boxed{\bf\,a^2-b^2=(a-b)(a+b)}\\\\=(a-b)(a+b)-(a-b)\\\\\text{By taking (a-b) as a common factor}\\\\=(a-b)(a+b-1)\\\\\\\textbf{Answer:}\\\\\textbf{The factors of \bf\,a(a-1)-b(b-1) are (a-b) and (a+b-1)}$

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Answer 2

Step-by-step explanation:

a(a-1)-b(b-1)

a²-b²-(a-b)

(a-b)(a+b)-(a-b)

(a-b)(a+b-1)