Question

Write the expression as a product:

1–(2x–1)^2

Answer 1

`1- ( { 2 x - 1)}^(2) = 4x (1 - x )`

Explanation:

We want to to rewrite

`1 - ( { 2 x - 1)}^(2)`

Use difference of two squares to get:

`{a}^(2) - {b}^(2) = (a + b)(a - b)`

This implies that:

`{1}^(2) - ( { 2 x - 1)}^(2) = (1 +( 2x - 1))(1 - (2x - 1))`

`{1}^(2) - ( { 2 x - 1)}^(2) = (1 + 2x - 1)(1 - 2x + 1)`

This finally simplifies to:

`{1}^(2) - ( { 2 x - 1)}^(2) = 2x (2 - 2x )`

Therefore the required product is

`2x (2 - 2x ) = 4x(1 - x)`