Question

(x+y^2)^2-(y^2) (y^2+2)-2xy^2Упростите выражение При х=-5​

Answer 1

(х+у^2)^2 -у^2 ×(у^2 +2)-2ху^2=х^2 +2ху^2 +у^4 -у^4 -2у^2 -2ху^2=х^2 -2у^2

Answer 2

To simplify the expression, let's substitute the value of x with -5 and then perform the calculations:

Given expression: (x + y^2)^2 - y^2(y^2 + 2) - 2xy^2

Substitute x = -5:

((-5) + y^2)^2 - y^2(y^2 + 2) - 2(-5)y^2

Now, simplify each term step by step:

1. Simplify the first term: ((-5) + y^2)^2 ((-5) + y^2)^2 = (y^2 - 5)^2 = y^4 - 10y^2 + 25

2. Simplify the second term: y^2(y^2 + 2) y^2(y^2 + 2) = y^4 + 2y^2

3. Simplify the third term: -2xy^2 -2(-5)y^2 = 10y^2

Now, the simplified expression becomes:

(y^4 - 10y^2 + 25) - (y^4 + 2y^2) - 10y^2

Next, combine like terms:

y^4 - 10y^2 + 25 - y^4 - 2y^2 - 10y^2

Now, simplify further:

y^4 - y^4 - 10y^2 - 2y^2 - 10y^2 + 25

Combine like terms again:

-22y^2 + 25

So, the simplified expression for x = -5 is:

-22y^2 + 25