Respuesta :

ANSWER

[tex](x - 5) ^{5} = {x}^{5} - 25 {x}^{4} + 250 {x}^{3} - 1250 {x}^{2} + 3125x- 3125[/tex]

EXPLANATION

From the Pascal's triangle,

The coefficients are :

1, 5, 10,10, 5,1

Because of the negative sign, the expansion will alternate sign.

[tex](x - y) ^{5} = {x}^{5} - 5 {x}^{4} y + 10 {x}^{3} {y}^{2} - 10 {x}^{2} {y}^{3} + 5x {y}^{4} - {y}^{5} [/tex]

We now put y=5 into the expansion to get,

[tex](x - 5) ^{5} = {x}^{5} - 5 {x}^{4} (5) + 10 {x}^{3} ( {5}^{2}) - 10 {x}^{2} ({5})^{3} + 5x( {5})^{4} - {5}^{5} [/tex]

[tex](x - 5) ^{5} = {x}^{5} - 25 {x}^{4} + 250 {x}^{3} - 1250 {x}^{2} + 3125x- 3125[/tex]

Answer:

(x - 5)^5 = x^5 - 25x^4 + 250x³ - 1250x² + 3125x - 3125

Step-by-step explanation:

The explanation in the attached file

Ver imagen Ashraf82