Question

Zapisz w najprostszej postaci:

a)(x+3y)²-9y²

b)4x²+1-(2x+1)²

c)2(3+b)²-12b

d)(x-2)²-(x+1)²

Answer 1

a)
(x + 3y)² - 9y² =
= x² + 6xy + 9y² - 9y² =
= x² + 6xy =
= x(x + 6y)

b)
4x² + 1 - (2x + 1)² =
= 4x² + 1 - (4x² + 4x + 1) =
= 4x² + 1 - 4x² - 4x - 1 =
= -4x

c)
2(3 + b)² - 12b =
= 2(9 + 6b + b²) - 12b =
= 18 + 12b + 2b² - 12b =
= 2b² + 18 =
= 2(b² + 9)

d)
(x - 2)² - (x + 1)² =
= (x² - 4x + 4) - (x² + 2x + 1) =
= x² - 4x + 4 - x² - 2x - 1 =
= -6x + 3