Question

(1/2а-b)(1/4a2+1/2ab+b2)-1/8a3

Answer 1

(1/2а-b)(1/4a²+1/2ab+b²)-1/8a³=1/8а³-b³-1/8a³=-b³

Answer 2

To simplify the expression:

(1/2a - b)(1/4a^2 + 1/2ab + b^2) - 1/8a^3

Let's start by multiplying the two binomials:

(1/2a - b)(1/4a^2 + 1/2ab + b^2) = (1/2a)(1/4a^2 + 1/2ab + b^2) - b(1/4a^2 + 1/2ab + b^2)

Now, distribute the terms:

= (1/8a^3 + 1/4ab + 1/2a^2b) - (1/4ab^2 + 1/2b^3)

Next, simplify the expression by combining like terms:

= 1/8a^3 + 1/4ab + 1/2a^2b - 1/4ab^2 - 1/2b^3

Finally, subtract 1/8a^3 from the expression:

= 1/8a^3 + 1/4ab + 1/2a^2b - 1/4ab^2 - 1/2b^3 - 1/8a^3

= (1/8a^3 - 1/8a^3) + 1/4ab + 1/2a^2b - 1/4ab^2 - 1/2b^3

= 0 + 1/4ab + 1/2a^2b - 1/4ab^2 - 1/2b^3

= 1/4ab + 1/2a^2b - 1/4ab^2 - 1/2b^3

So, the simplified expression is 1/4ab + 1/2a^2b - 1/4ab^2 - 1/2b^3.