Question

(4у^2+3)^2+(9-4у^2)^2-2(4у^2+3)(4у^2-9)

Answer 1

Ответ:

= (16y^4+9) + (81-16y^4)-(8y^2+6)(4y^2-9)= 16y^4 + 9 + 81 - 16Y^4- 32y^4 - 72 y^2 + 24y^2-54= 90-32y^4-72y^2+24y^2-54= -32y^4-48y^2 + 36

Объяснение:

Answer 2

To simplify the given expression, let's work step by step:

1. Expand (4у^2+3)^2: (4у^2+3)^2 = (4у^2+3) * (4у^2+3) = 4у^2 * 4у^2 + 4у^2 * 3 + 3 * 4у^2 + 3 * 3 = 16у^4 + 12у^2 + 9

2. Expand (9-4у^2)^2: (9-4у^2)^2 = (9-4у^2) * (9-4у^2) = 9 * 9 - 4у^2 * 9 - 4у^2 * 9 + 4у^2 * 4у^2 = 81 - 36у^2 - 36у^2 + 16у^4 = 16у^4 - 72у^2 + 81

3. Expand 2(4у^2+3)(4у^2-9): 2(4у^2+3)(4у^2-9) = 2 * (4у^2 * 4у^2 + 4у^2 * (-9) + 3 * 4у^2 + 3 * (-9)) = 2 * (16у^4 - 36у^2 + 12у^2 - 27) = 2 * (16у^4 - 24у^2 - 27)

Now, we can combine all the expanded terms:

(4у^2+3)^2 + (9-4у^2)^2 - 2(4у^2+3)(4у^2-9) = (16у^4 + 12у^2 + 9) + (16у^4 - 72у^2 + 81) - 2 * (16у^4 - 24у^2 - 27)

Now, combine like terms:

= 16у^4 + 12у^2 + 9 + 16у^4 - 72у^2 + 81 - 32у^4 + 48у^2 + 54

Now, further simplify:

= 16у^4 + 16у^4 - 32у^4 + 12у^2 - 72у^2 + 48у^2 + 9 + 81 + 54

= 0у^4 - 12у^2 + 144 + 54

Finally:

= -12у^2 + 198

So, the simplified expression is -12у^2 + 198.