diabb
diabb diabb
  • 10-03-2020
  • Mathematics
contestada

Write the expression as a product:

1–(2x–1)^2

Respuesta :

kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 18-03-2020

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]

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