1. We start with the expression: $$4y(3x-1)+(3x-1)^2$$ 2. Notice that both terms contain the factor $(3x-1)$. 3. Factor $(3x-1)$ out: $$ (3x-1)(4y+(3x-1)) $$ 4. Simplify inside the parentheses: $$ (3x-1)(4y+3x-1) $$ The factorised form is $$ (3x-1)(4y+3x-1) $$.