Question

Desenvolva esse binômios:

(1 + 3a/2 ) ^ 6
(1/x² + x ) ^ 3

Answer 1

Primeira Equação: (1+3a/2) ^ 6 = (6,0)1^6 x (3a/2)^0 + (6,1)1^5 x (3a/2)^1 + (6,2)1^4 x (3a/2)^2 + (6,3)1^3 x (3a/2)^3 + (6,4)1^2 x (3a/2)^4 + (6,5)1^1 x (3a/2)^5 + (6,6)1^0 x (3a/2)^6= 1×1⁶×1+ 6×1⁵×3a/2+12×1⁴×9a²/4+20×1³×27a³/8+15×1²×81a⁴/16+6×1¹×243a⁵/32+1×1×729a⁶/64=1+9a+27a²+540a³/8+1215a⁴/16+1458a⁵/32+729a⁶/64=1+9a+27a²+135a³/2+1215a⁴/16+729a⁵/16+729a⁶/64.

Segunda: (1/x² + x )³= (3,0)(1/x²)³×(x)⁰+(3,1)(1/x²)²×(x)¹+(3,2)(1/x²)¹×(x)²+(3,3)(1/x²)⁰×(x)³=1×(1/x⁶)×1+3×(1/x⁴)×x+3×(1/x²)×x²+1×1×x³=1/x⁶+3x/x⁴+3x²/x²+x³=1/x⁶+3/x³+3+x³

Espero que entenda esta confusão :D