Question

(2mn-1)^3+1 (3a-2b)^3+8b^3

Answer 1

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Answer 2

To expand the given expressions, let's start with the first expression:

(2mn - 1)^3 + 1

We can expand this expression using the binomial expansion formula:

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

In this case, a = 2mn and b = -1. Applying the formula, we have:

(2mn)^3 + 3(2mn)^2(-1) + 3(2mn)(-1)^2 + (-1)^3 + 1

Expanding each term:

8m^3n^3 + 3(4m^2n^2)(-1) + 3(2mn)(1) + (-1) + 1

Simplifying further:

8m^3n^3 - 12m^2n^2 + 6mn

Now, let's expand the second expression:

(3a - 2b)^3 + 8b^3

Again, using the binomial expansion formula:

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

In this case, a = 3a and b = -2b. Applying the formula, we have:

(3a)^3 + 3(3a)^2(-2b) + 3(3a)(-2b)^2 + (-2b)^3 + 8b^3

Expanding each term:

27a^3 + 3(9a^2)(-2b) + 3(3a)(4b^2) + (-8b^3) + 8b^3

Simplifying further:

27a^3 - 54a^2b + 36ab^2

Therefore, the expanded forms of the given expressions are:

(2mn - 1)^3 + 1 = 8m^3n^3 - 12m^2n^2 + 6mn

(3a - 2b)^3 + 8b^3 = 27a^3 - 54a^2b + 36ab^2