Question

Zapisz w jak najprostszej postaci:
x(5x-2)-2x(x+1)=
(a+2)²-(a-2)²
(a+2b)(2a-b)-3a=
(a+√2)(a-√2)-2(a²-1)
(p-⅓)³+(p+⅓)²

Answer 1

1) x(5x-2)-2x(x+1)=5x²-2x-2x²-2x=3x²-4x
2) (a+2)²-(a-2)²= a²+4a+4-(a²-4a+4) = a²+4a+4-a²+4a-4=8a
3) (a+2b)(2a-b)-3a=2a²-ab+4ab-2b²-3a=2a²+3ab-2b²-3a
4) (a+√2)(a-√2)-2(a²-1) =a²-a√2+a√2-2-2a²+2=-a²
5) (p-⅓)³+(p+⅓)²=(p-1/3)(p-1/3)(p-1/3) + (p+1/3)(p+1/3) =
=p³-1/3p²-1/9p-1/27-1/3p²-1/9p+p²+1/3p+1/3p+1/9=
=p³-2/3p²-2/9p-1/27+p²+2/3p+1/9=p³+2/3p²+4/9+2/27

Answer 2

5x²-4x-2x²=8

Answer 3

X(5x -2) -2x(x +1) =5x² -2x -2x²-2x =3x² -4x
(a+2)² - (a - 2)² = a² +4a +4 -a²+4a -4 = 8a
(a +2b)(2a - b) - 3a =2a² -ab +4ab -2b² = 2a²+3ab -2b²
(a +√2)(a -√2) - 2(a² -1) = a² -2 -2a²+2 = -a²
(p -1/3)² + (p+1/3)² = p² - (2/3}p +1/9 + p² +(2/3)p +1/9 =
= 2p² + 2/9