Question

Simplifique as expressoes A) (a+b)²+(a-b)² B) (x-2)²+x²-2(x-1)² C) (m-1)²-(m+1).(m-1) D) (a+1)³-(a-2)³

Answer 1

a) (a + b)² + (a - b)²

= a² + 2ab + b² + a² - 2ab + b²
= 2a² + 2b²
= 2.(a² + b²)

b) (x - 2)² + x² - 2(x - 1)²

= x² - 4x + 4 + x² - (x² - 2x + 1)

= 2x² - 4x + 4 - x² + 2x - 1

= x² - 2x + 3

c) (m - 1)² - (m+1).(m-1)

= m² - 2m +1 - (m² - m + m - 1)

= m² - 2m + 1 - m² + 1

= -2m + 2

= -2(m-1)

d) (a+1)³ - (a-2)³

= (a+1)².(a+1) - (a-2)².(a-2)

= (a² + 2a + 1).(a+1) - (a² - 2a + 4) . (a-2)

= a³ + a² + 2a² + 2a + a + 1 - (a³ - 2a² - 2a² + 4a + 4a - 8)

= a³ + 3a² + 3a + 1 - (a³ - 4a² + 5a - 8)

= a³ + 3a² + 3a + 1 - a³ + 4a² - 5a + 8

= 7a² - 2a + 9