Question

A)(6a+2b)^2-24abb)-6x^3-3(x^3-1)^2

Answer 1

$a)\;(6a+2b)^2-24ab=36a^2+24ab+4b^2-24ab=36a^2+4b^2\\\\ b)\;-6x^3-3(x^3-1)^2=-3(2x^3+(x^3-1)^2)=\\=-3(2x^3+x^6-2x^3+1)=-3(x^6+1)$

Answer 2

It seems like you have an algebraic expression, and you'd like to simplify it. Let's break it down step by step:

A) (6a + 2b)^2 - 24ab + (-6x^3) - 3(x^3 - 1)^2

First, let's simplify the square of the binomial (6a + 2b)^2:

(6a + 2b)^2 = (6a)^2 + 2 * (6a) * (2b) + (2b)^2 = 36a^2 + 24ab + 4b^2

Now, substitute this back into the original expression:

A) = (36a^2 + 24ab + 4b^2) - 24ab - 6x^3 - 3(x^3 - 1)^2

Now, distribute the -3 into the second term:

A) = 36a^2 + 24ab + 4b^2 - 24ab - 6x^3 - 3(x^3 - 1)^2

Next, simplify the terms with 'ab':

A) = 36a^2 + (24ab - 24ab) + 4b^2 - 6x^3 - 3(x^3 - 1)^2

The terms (24ab - 24ab) cancel out:

A) = 36a^2 + 4b^2 - 6x^3 - 3(x^3 - 1)^2

Now, let's simplify the last part by expanding (x^3 - 1)^2:

A) = 36a^2 + 4b^2 - 6x^3 - 3(x^3 - 1)(x^3 - 1)

A) = 36a^2 + 4b^2 - 6x^3 - 3(x^6 - 2x^3 + 1)

Now distribute the -3 into the second term within the parentheses:

A) = 36a^2 + 4b^2 - 6x^3 - 3x^6 + 6x^3 - 3

Now, simplify the terms with 'x^3':

A) = 36a^2 + 4b^2 - 3x^6 - 3

So, the simplified expression is:

A) = 36a^2 + 4b^2 - 3x^6 - 3