Question

(2x +3)² -(5x-1)² factorizar binomio

Answer 1

Respuesta:

( - 7x - 4 ) ( 3x - 2 )

Explicación paso a paso:

( 2x + 3 )²

= ( 2x )² + 3² + 2 ( 2x ) ( 3 )

= 4x² + 9 + 12x

( 5x - 1 )²

= ( 5x )² + 1² - 2 ( 5x ) ( 1 )

= 25x² + 1 - 10x

( 2x + 3 )² - ( 5x - 1 )²

= 4x² + 9 + 12x - ( 25x² + 1 - 10x )

= 4x² + 9 + 12x - 25x² - 1 + 10x

= 4x² - 25x² + 12x - 10x + 9 - 1

= - 21x² + 2x + 8

- 21x² + 2x + 8 = 0

21x² - 2x - 8 = 0

21x² + 12x - 14x - 8 = 0

3x ( 7x + 4 ) - 2 ( 7x + 4 ) = 0

( 7x + 4 ) ( 3x - 2 )

( 7x + 4 ) ( 3x - 2 ) = ( - 7x - 4 ) ( 3x - 2 )