Question

Write the expression as a product: 1–(2x–1)^2

Answer 1

Answer:

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

Step-by-step 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

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