Question

Factorization: $(2a-3{)}^2-2(2a-3\left)\right(a-1)+(a-1{)}^2$

• A. $(2a-3{)}^2$
• B. $(a-2{)}^2$
• C. $(a-1{)}^2$
• D. $(a-3{)}^2$

Answer 1

The correct option is B $(a-2{)}^2$

$\Rightarrow (2a-3{)}^2-2(2a-3\left)\right(a-1)+(a-1{)}^2$

$\text{Let}x=(2a-3),y=(a-1)$

$\Rightarrow x^2-2xy+y^2$

$\Rightarrow (x-y{)}^2$

$\Rightarrow \text{Substituting the values of x and y,we get}$

$\Rightarrow \left(\right(2a-3)-(a-1){)}^2$

$\Rightarrow (2a-3-a+1{)}^2$

$\Rightarrow (a-2{)}^2$