Question

Wykonaj działania.Wynik podaj w najprostszej postaci.

Answer 1

a)

(x + 1)² - (x - 1)² + (x + 2)² + (2 - x)² =

= [(x + 1)+(x - 1)]*[(x + 1)-(x - 1)] + 2x² + 8

= [2x]*[2] + 2x² + 8 = 2x² + 4x + 8 = 2(x² + 2x + 4) =

= 2(x + 2)²

b)

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

= 2(3 + x)² - (2 - x)² -3(4 - x²) =

= 2(9 + x² + 6x) - (4 + x² - 4x)- 12 + 3x² =

= 18 + 2x² + 12x - 4 - x² + 4x - 12 + 3x² =

= 2 + 4x² + 16x = 2(2x² + 8x + 1)
 
c) 

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

= 16x² - 9y² - 2(16x² + 9y² + 24xy) + 2(9x² + 16y² - 24xy) =

= 16x² - 9y² - 32x² - 18y² - 48xy + 18x² + 32y² - 48xy =

= 2x² + 5y² - 96xy