Question

(a-2b) ²-(a-b)*(a +b)​

Answer 1

$(a-2b)^2-(a-b)(a+b)=a^2-4ab+4b^2-(a^2-b^2)=\\=a^2-4ab+4b^2-a^2+b^2=b^2-4ab+4b^2=5b^2-4ab.$

Answer 2

$\boxed{ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }\\ \boxed{ {a}^{2} - {b}^{2} = (a - b)(a + b)}$

${(a - 2b)}^{2} - (a - b)(a + b) = {a}^{2} - 4ab + 4 {b}^{2} - ( {a}^{2} - {b}^{2} ) = \cancel{{a}^{2}} - 4ab + 4 {b}^{2} \cancel{- {a}^{2}} + {b}^{2} = \boldsymbol{- 4ab + 5 {b}^{2} }$