Question

Раскрыть скобки (3a-7c)^2 (2b^2+a2)^2

Answer 1

9а^2 - 42ас+49с^2

4b^4+4b^2 a^2 +a^4

Answer 2

To expand the given expression, you can use the formula for squaring a binomial:

For any binomial expression (x + y)^2, the result is x^2 + 2xy + y^2.

Now let's apply this formula to each part of the expression:

1. (3a - 7c)^2: (3a - 7c)^2 = (3a)^2 - 2 * (3a) * (7c) + (7c)^2 = 9a^2 - 42ac + 49c^2

2. (2b^2 + a^2)^2: (2b^2 + a^2)^2 = (2b^2)^2 + 2 * (2b^2) * (a^2) + (a^2)^2 = 4b^4 + 4a^2b^2 + a^4

Now, let's combine the two results:

(3a - 7c)^2 * (2b^2 + a^2)^2 = (9a^2 - 42ac + 49c^2) * (4b^4 + 4a^2b^2 + a^4)

To simplify it further, you can perform multiplication between the terms of the two expressions:

(9a^2 - 42ac + 49c^2) * (4b^4 + 4a^2b^2 + a^4) = = 9a^2 * 4b^4 + 9a^2 * 4a^2b^2 + 9a^2 * a^4 - 42ac * 4b^4 - 42ac * 4a^2b^2 - 42ac * a^4 + 49c^2 * 4b^4 + 49c^2 * 4a^2b^2 + 49c^2 * a^4

Now, simplify each term:

= 36a^2b^4 + 36a^4b^2 + 9a^6 - 168a^3bc^2 - 42a^5c - 42a^3c^3 + 196c^2b^4 + 196a^2c^2b^2 + 49a^4c^2

So the expanded expression is:

36a^2b^4 + 36a^4b^2 + 9a^6 - 168a^3bc^2 - 42a^5c - 42a^3c^3 + 196c^2b^4 + 196a^2c^2b^2 + 49a^4c^2