Question

Alexa uses the binomial theorem to correctly expand (x+2)^4. which is one of the terms in alexa's answer?

Answer 1

^0 ...............1
^1..............1  1
^2............1  2  1 
^3...........1 3  3  1
^4..........1 4 6  4  1

(x+2)^4 = 1(x)^4(2)^0 + 4(x)^3(2)^1 + 6(x)^2(2)^2 + 4(x)^1(2)^3 + 1(x)^0(2)4
             = $x^{4} + 8 x^{3} + 24 x^{2} + 32x + 16$

Answer 2

Alexa's answer is: $(x+2)^4=x^4+8x^3+24x^2+32x+16$.

Using the binomial theorem we get:

$(x+2)^4 \\\\=(4C0)(x)^4(2)^0 + (4C1)(x)^3(2)^1 + (4C2)(x)^2(2)^2 + (4C3)(x)^1(2)^3 + (4C4)(x)^0(2)^4\\\\= 1(x)^4(2)^0 + 4(x)^3(2)^1 + 6(x)^2(2)^2 + 4(x)^1(2)^3 + 1(x)^0(2)^4\\\\=x^4+8x^3+24x^2+32x+16$

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