Question

(x + 2)4 = x4 + 8x3 +... Use the Binomial Theorem to complete the binomial expansion. Enter only the next three terms; use the ^ key for exponents, example: 10x^2+20x+30.

Answer 1

(x+2)^4=((x+2)^2)^2(x+2)^2=(x^2+2^2+2(x)(2))= x^2+4+4x (x^2+4+4x)^2=(x^2+4+4x)(x^2+4+4x) = x^4+4x^2+4x^3+4x^2+16+16x+4x^3+16x+16x^2=x^4+4x^3+4x^3+4x^2+16x^2+4x^2+16x+16x+16=x^4+8x^3+24x^232x+16