8 Eliminați parantezele, reduceți termenii asemenea și calculați: X(a²-2a + 2) (a²- 3a + 1) + (a² + 2a − 1)(a² + a + 4); b (b²-3b-6) (b²+2b-3) - (2b²+b+5)(b-b² - 2); c (3a²b + 6ab²) (2a²b+8ab²) - (4a²b- 5ab²) (3a²b-7ab²); d (5a-2)(-3a² + a-3) - (3a²- 2a - 2) (4a² + 2a+3); e (a²-3b)(a + 3a²b + 9b²) - a²(a - b)-9b²(a - 3b).
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
a) (a²-2a + 2) (a²- 3a + 1) + (a² + 2a − 1)(a² + a + 4)= a⁴-3a³+a²-2a³+6a²-2a+2a²-6a+2+a⁴+4a²+2a³+2a²+8a-a²-a-4=
2a⁴-5a³+3a³+14a²-8a+7a+2-4= 2a⁴-2a³+14a²-a-2
b) (b²-3b-6) (b²+2b-3) - (2b²+b+5)(b-b² - 2)=
b⁴+2b³-3b²-3b³-6b²+9b-6b²-12b+18-(2b³-2b⁴-4b²+b²-b³-2b+5b-5b²-10)=
b⁴-b³-15b²-3b+18-(b³-2b⁴-8b²+3b-10)=
b⁴-b³-15b²-3b+18-b³+2b⁴+8b²-3b+10=3b⁴-2b³-7b²-6b+28
c) (3a²b + 6ab²) (2a²b+8ab²) - (4a²b- 5ab²) (3a²b-7ab²)=
3ab·(a+2b)·2ab·(a+4b)-ab·(4a-5b)·ab·(3a-7b)=
6a²b²(a+2b)(a+4b)-a²b²(4a-5b)(3a-7b)=
6a²b²(a²+4ab+2ab+8b²)-a²b²(12a²-15ab-28ab+35b²)=
6a²b²(a²+6ab+8b²)-a²b²(12a²-43ab+35b²)=
a²b²[6(a²+6ab+8b²)-(12a²-43ab+35b²)]=
a²b²(6a²+36ab+48b²-12a²+43ab-35b²)=
a²b²(-6a²+79ab+13b²)=
-6a⁴b²+79a³b³+13a²b⁴
d) (5a-2)(-3a²+a-3)-(3a²-2a-2)(4a²+2a+3)=
-15a³+5a²-15a+6a²-2a+6-(12a⁴+6a³+9a²-8a³-4a²-6a-8a²-4a-6)=
-15a³+11a²-17a+6-(12a⁴-2a³-3a²-10a-6)=
-15a³+11a²-17a+6-12a⁴+2a³+3a²+10a+6=-12a⁴-13a³+14a²-7a+12
e) (a²-3b)(a⁴ + 3a²b + 9b²) - a²(a - b)-9b²(a - 3b)=
a⁶+3a⁴b+9a²b²-3a⁴b-9a²b²-27b³-a³+a²b-9ab²+27b³=
a⁶-a³+a²b-9ab²