Question

desenvolva os binomios de newton:

a)(2x+5a)³
b)(x-1)^4

Answer 1

letra A)
$\binom{3}{0} {(2x)}^{3} {(5a})^{0} + \binom{3}{1}{(2x)}^{2} {(5a})^{1} + \binom{3}{2}{(2x)}^{1} {(5a})^{2} + \binom{3}{3}{(2x)}^{0} {(5a})^{3} \\ \\ 1 \times 8 {x}^{3} + (3 \times 4 {x}^{2} \times 5a) +( 3 \times 2x \times 25 {a}^{2}) + 1 \times 125 {a}^{3} \\ \\ 8 {x}^{3} + 60 {x}^{2} a + 150x {a}^{2} + 125 {a}^{3}$

letra B )
$\binom{4}{0}( {x})^{4} ( - 1)^{0} - \binom{4}{1}( {x})^{3} ( - 1)^{1} - \binom{4}{2}( {x})^{2} ( - 1)^{2} - \binom{4}{3}( {x})^{1} ( - 1)^{3} - \binom{4}{4}( {x})^{0} ( - 1)^{4} \\ \\ {x}^{4} - (4 \times {x}^{3} \times ( - 1)) - (6 \times {x}^{2} \times 1) - (4 \times x \times ( - 1)) - 1 \\ \\ {x}^{4} + 4 {x}^{3} - 6 {x}^{2} + 4x - 1$