Question

resolva as operações e apresente a resposta na forma reduzida:

a) (a+b)² - (a-2b)²

b) (2x-1)² + (x+3) (x-3)

c) ( a³ - 1)² - (a³- a) . (a³+a) + (a³ - 1)²

d) (1+m)² + (1-m)² + (-1+m)² + (-1-m)²

Answer 1

a) (a+b)² - (a-2b)²
= (a²+2ab+b²) - (a²-4ab+4b²)
= a²+2ab+b²-a²+4ab-4ab²
= b²+6ab-4ab²
= b²+ab(6-4ab)

b) (2x-1)² + (x+3) (x-3)
= (4x²-4x+1)+x²-9
= 4x²-4x+1+x²-9
= 5x²-4x-8
= x(5x-4)-8

c) ( a³ - 1)² - (a³- a) . (a³+a) + (a³ - 1)²
= (a^6-2a³+1)-(a^6-a²)+(a^6-2a³+1)
= a^6-2a³+1-a^6+a²+a^6-2a³+1
= a^6-4a³+a²+2

d) (1+m)² + (1-m)² + (-1+m)² + (-1-m)²
= (1+2m+m²)+(1-2m-m²)+(1-2m+m²)+(1+2m+m²)
= 1+2m+m²+1-2m-m²+1-2m+m²+1+2m+m²
= 2m²+4