Answer:
[tex]1- ( { 2 x - 1)}^{2} = 4x (1 - x )[/tex]
Step-by-step explanation:
We want to to rewrite
[tex]1 - ( { 2 x - 1)}^{2} [/tex]
Use difference of two squares to get:
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]
This implies that:
[tex]{1}^{2} - ( { 2 x - 1)}^{2} = (1 +( 2x - 1))(1 - (2x - 1))[/tex]
[tex]{1}^{2} - ( { 2 x - 1)}^{2} = (1 + 2x - 1)(1 - 2x + 1)[/tex]
This finally simplifies to:
[tex]{1}^{2} - ( { 2 x - 1)}^{2} = 2x (2 - 2x )[/tex]
Therefore the required product is
[tex] 2x (2 - 2x ) = 4x(1 - x)[/tex]
