Expand (3-x) (2+x)^3 by using a binomial expansion
To expand (3-x) (2+x)^3 using the binomial expansion, we first need to apply the binomial theorem. The binomial theorem states that for any positive integer n:
(a+b)^n = nC0 * a^n * b^0 + nC1 * a^(n-1) * b^1 + nC2 * a^(n-2) * b^2 + ... + nCn * a^0 * b^n
In this case, a = 2+x and b = 3-x. Therefore:
(3-x) (2+x)^3 = (2+x)^3 * 3 - (2+x)^3 * x
Now, we can expand each term in the expression (2+x)^3 separately using the binomial theorem:
(2+x)^3 = 3C0 * 2^3 * x^0 + 3C1 * 2^2 * x^1 + 3C2 * 2^1 * x^2 + 3C3 * 2^0 * x^3
(2+x)^3 = 8 + 12x + 6x^2 + x^3
Now, we can substitute this back into our original expression:
(3-x) (2+x)^3 = (8 + 12x + 6x^2 + x^3) * 3 - (8 + 12x + 6x^2 + x^3) * x
Expanding this further will give us the final expanded form of (3-x) (2+x)^3.