Answer to Question #346437 in Algebra for bookaddict

Question

Find the first 3 terms, in ascending powers of 𝑥, of the binomial expansion of (2−𝑥)⁴ and simplify each term.

Answer 1

$(a+b)^4=\dbinom{4}{0}a^4+\dbinom{4}{1}a^3b+\dbinom{4}{2}a^2b^2$ $+\dbinom{4}{3}ab^3+\dbinom{4}{4}b^4$ $=a^4+4a^3b+6a^2b^2+4ab^3+b^4$

$(2-x)^4=16-32x+24x^2-8x^3+x^4$

$16, -32x, 24x^2$