Question

4n(5n+3)^2-n(10n+1)^2

Answer 1

Вот правильный ответ)

Answer 2

To simplify the expression 4n(5n+3)^2 - n(10n+1)^2, let's break it down step by step.

Step 1: Expand the squared terms. (5n+3)^2 = (5n+3)(5n+3) = 25n^2 + 15n + 15n + 9 = 25n^2 + 30n + 9

(10n+1)^2 = (10n+1)(10n+1) = 100n^2 + 10n + 10n + 1 = 100n^2 + 20n + 1

Step 2: Apply the distributive property. 4n(5n+3)^2 - n(10n+1)^2 = 4n(25n^2 + 30n + 9) - n(100n^2 + 20n + 1)

Step 3: Simplify each term. 4n(25n^2 + 30n + 9) = 100n^3 + 120n^2 + 36n n(100n^2 + 20n + 1) = 100n^3 + 20n^2 + n

Step 4: Combine like terms. 100n^3 + 120n^2 + 36n - (100n^3 + 20n^2 + n) = 100n^3 - 100n^3 + 120n^2 - 20n^2 + 36n - n

Step 5: Simplify further. The terms 100n^3 and -100n^3 cancel each other out, leaving: 120n^2 - 20n^2 + 36n - n = 100n^2 + 35n

Therefore, the simplified form of the expression 4n(5n+3)^2 - n(10n+1)^2 is 100n^2 + 35n.