Question

expand
(x+5) raise to 4

Answer 1

use the coefficients from Pascals triangle 1, 4, 6, 5, 4, 1

then its

\[1 \times x^4 + 4 \times x^3 \times 5 + 6 \times x^2 \times 5^2 + 4 \times x \times5^3 + 5^4\]


simplifying gives

\[(x + 5)^4 = x^4 + 20x^3 + 150x^2 + 500x + 625\]

or you could use binomial expansion

\[^{n}C _{r} x^{n - r} 5^r\]