Question

Aduceți la forma cea mai simplă

Answer 1

$a) \\ \\ ( {a}^{3} - 1)( {a}^{6} + {a}^{3} + 1) = \\ \\ {a}^{3}( {a}^{6} + {a}^{3} + 1) - ( {a}^{6} + {a}^{3} + 1) = \\ \\ {a}^{9} + {a}^{6} + {a}^{3} - {a}^{6} - {a}^{3} - 1 = \\ \\ {a}^{9} + ( {a}^{6} - {a}^{6}) + ( {a}^{3} - {a}^{3}) - 1 = \\ \\ {a}^{9} - 1$

b)

(m-1)(m²+m+1)=

m(m²+m+1)-(m²+m+1)=

m³+m²+m-m²-m-1=

m³+(m²-m²)+(m-m)-1=

m³-1

$c) \\ \\ ( {a}^{2} + 1)( {a}^{4} - {a}^{2} + 1) = \\ \\ {a}^{2}( {a}^{4} - {a}^{2} + 1) + {a}^{4} - {a}^{2} + 1 = \\ \\ {a}^{6} - {a}^{4} + {a}^{2} + {a}^{4} - {a}^{2} + 1 = \\ \\ {a}^{6} + ( - {a}^{4} + {a}^{4}) + ( {a}^{2} - {a}^{2}) + 1 = \\ \\ {a}^{6} + 1$

d)

(2a+3b)(4a²-6ab+9b²)=

2a(4a²-6ab+9b²)+3b(4a²-6ab+9b²)=

8a³-12a²b+18ab²+3b(4a²-6ab+9b²)=

8a³-12a²b+18ab²+12ba²-18b²a+27b³=

8a³+(-12a²b+12a²b)+(18ab²-18ab²)+27b³=

8a³+27b³