Question

(3а-а²)²-а²(а-2)(а+2)+2а(7+3а²)

Answer 1

(3а-а²)²-а²(а-2)(а+2)+2а(7+3а²)=(3а)²-2*3а*а²+(а²)²-а²(а²-4)+14а+6а³=3а²-6а³+а в четвертой степени-а в четвертой степени+4а²+14а+6а³=7а²+14а.

Answer 2

To simplify the given expression:

(3a - a^2)^2 - a^2(a - 2)(a + 2) + 2a(7 + 3a^2)

First, expand each term:

(3a - a^2)^2 = (3a - a^2)(3a - a^2) = 9a^2 - 3a^3 - 3a^3 + a^4 = a^4 - 6a^3 + 9a^2

a^2(a - 2)(a + 2) = a^2(a^2 - 4) = a^4 - 4a^2

2a(7 + 3a^2) = 14a + 6a^3

Now, substitute these expanded forms back into the original expression:

(a^4 - 6a^3 + 9a^2) - (a^4 - 4a^2) + (14a + 6a^3)

Now, simplify the expression:

a^4 - 6a^3 + 9a^2 - a^4 + 4a^2 + 14a + 6a^3

Now, you can see that the a^4 terms cancel out:

-6a^3 + 9a^2 - 6a^3 + 4a^2 + 14a

Now, combine like terms:

(-6a^3 - 6a^3) + (9a^2 + 4a^2) + 14a

-12a^3 + 13a^2 + 14a

So, the simplified expression is:

-12a^3 + 13a^2 + 14a