Question

1) Efetue:
a) (x + 1)(x - 1) + (x + 2)(x - 2)
b) (x + y)² - (2x + 2y)² + (3x + 3y)²
c)(x + y)(x - y) + (x - y)² - (x + y)²
d) (x + 2)² - 2(x + 2)(x - 2) + (x - 2)²
​

Answer 1

a) (x + 1)(x - 1) + (x + 2)(x - 2)

x²-1+x²-4

2x²-5

b) (x + y)² - (2x + 2y)² + (3x + 3y)²

x²+2xy+y²-(4x²+8xy+4y²)+9x²+18xy+9y²

x²+2xy+y²-4x²-8xy-4y²+9x²+18xy+9y²

6x²+20xy+y²-8xy-4y²+18xy+9y²

6x²+12xy+y²-4y²+9y²

6x²+12xy+6y²

c)(x + y)(x - y) + (x - y)² - (x + y)²

x²-y²+(x-y)²-(x+y)²

x²-y²+(-2y)×2x

x²-y²-4xy

d) (x + 2)² - 2(x + 2)(x - 2) + (x - 2)²

x²+4x+4-2(x²-4)+x²-4x+4

x²+4x+4-2x²+8+x²-4x+4

x²+4-2x²+8+x²+4

0+4+8+4

0+16

16