simplifique as expressões a seguir:
a) ( x + 1 )2+ ( x + 2 )2
b) ( 2x + 1 )2+ ( 3x + 1 )2
c) ( x – 4 )2– ( x – 1 )2
d) ( x + 1 )2– ( x – 2 )2
e) ( m – 1 )2– ( m + 1 ) . ( m – 1 ) f) ( x + 4 ) . ( x – 4) – ( x – 4 )2
Soluções para a tarefa
Resposta:
Explicação passo-a-passo:
a) ( x + 1 )^2+ ( x + 2 )^2
= x^2 + 2x + 1 + x^2 + 2.2.x + 4
= x^2 + 2x + 1 + x^2 + 4x + 4
= 2x^2 + 6x + 5
_________________
b) ( 2x + 1 )^2+ ( 3x + 1 )^2
= 4x^2 + 2.2x + 1 + 9x^2 + 2.3x + 1
= 13x^2 + 4x + 6x + 2
= 13x^2 + 10x + 2
________________
c) ( x – 4 )^2– ( x – 1 )^2
= x^2 - 2.4.x + 16 - [x^2 - 2x + 1]
= x^2 - 8x + 16 - x^2 + 2x - 1
= - 6x + 15
____________
d) ( x + 1 )^2 – ( x – 2 )^2
= x^2 + 2x + 1 - [x^2 - 2.2x + 4]
= x^2 + 2x + 1 - [ x^2 - 4x + 4]
= x^2 + 2x + 1 - x^2 + 4x - 4
= 6x - 3
_______________
e) ( m – 1 )^2 – ( m + 1 ) . ( m – 1 )
= m^2 - 2m + 1 - [m^2 - 1]
= m^2 - 2m + 1 - m^2 + 1
= - 2m + 2
_______________
f) ( x + 4 ) . ( x – 4) – ( x – 4 )^2
= x^2 + 16 - [x^2 - 2.4.x + 16]
= x^2 + 16 - [x^2 - 8x + 16]
= x^2 + 16 - x^2 + 8x - 16
= 8x