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

i am solving this without binomial theorem since i don;t know much about this :
(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

Answer 2

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

Answer 3

got it bonita
the answer is \[x^4+8x^3+32x+16\]