Question 1172645
Use the Binomial Theorem to expand the binomial and express the result in simplified form. (x + 4)3
<pre>(x + 4)3 should be (x + 4)<sup>3</sup>
{{{matrix(1,5, (a + b)^n, "=", ""[n]C[o](a)^(n - 0)(b)^o + ""[n]C[1](a)^(n - 1)(b)^1 + ""[n]C[2](a)^(n - 2)(b)^2, "........", ""nC[n](a)^(n - n)(b)^n)}}} <====== Binomial Expansion Formula
In this case, there are 4 terms, so we get:
{{{highlight_green(system(matrix(1,3, (a + b)^n, "=", ""[n]C[0](a)^(n - 0) (b)^0 + ""[n]C[1](a)^(n - 1)(b)^1 + ""[n]C[2] (a)^(n - 2)(b)^2 + ""[n]C[3](a)^(n - 3)(b)^3), matrix(1,3, (x + 4)^3, "=", ""[3]C[0](x)^(3 - 0)(4)^0) + ""[3]C[1](x)^(3 - 1)(4)^1 + ""[3]C[2](x)^(3 - 2)(4)^2 + ""[3]C[3](x)^(3 - 3)(4)^3, matrix(1,3, (x + 4)^3, "=", 1(x)^3(1) + 3(x)^2 * 4 + 3(x)^1 * (4)^2 + 1(x)^0 * 4^3), matrix(1,6, (x + 4)^3, "=", highlight(x^3 + 12x^2 + 48x + 64), "<=====", CORRECT, ANSWER)))}}}
There're only 4 terms so it's quite easy to EXPAND the binomial, in order to check this answer!