Question

Expand the expression (a + b)^3a + b ka whole cube.

A. (a^4 + b^4)
B. (a^3 + 3a^2b + 3ab^2 + b^3)
C. (a^3 + 3a^2b + 3ab^2 + b^3)
D. (a^3 + b^3 + 3a^2 + 3b^2)

Answer 1

To expand the expression (a + b)^3a + b ka whole cube, we first expand (a + b)^3 using the binomial theorem. Next, we multiply this expression by a + b ka whole cube and simplify the resulting expression by distributing and combining like terms.

Step-by-step explanation:

To expand the expression (a + b)^3a + b ka whole cube, we first expand (a + b)^3 using the binomial theorem.

The binomial theorem states that for any two numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n, 0)a^n + C(n, 1)a^(n-1)b + C(n, 2)a^(n-2)b^2 + ... + C(n, n)b^n

Using this theorem, the expansion of (a + b)^3 is:

(a + b)^3 = C(3, 0)a^3 + C(3, 1)a^2b + C(3, 2)ab^2 + C(3, 3)b^3

Simplifying this expression gives us:

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

Next, we multiply this expression by a + b ka whole cube:

(a + b ka)^3 = (a^3 + 3a^2b + 3ab^2 + b^3)(a + b ka)(a + b ka)

Expanding this expression gives us:

(a + b ka)^3 = (a^3 + 3a^2b + 3ab^2 + b^3)(a^2 + 2abka + b^2k^2a^2)

From here, you can continue to simplify the expression by distributing and combining like terms.