Question

(y^2-2y)^2-y^2(y+3) (y-3)+2y (2y^2+5)

Answer 1

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Answer 2

Let's simplify the given expression step by step:

Expression: (y^2 - 2y)^2 - y^2(y + 3)(y - 3) + 2y(2y^2 + 5)

Step 1: Expand the squared term (y^2 - 2y)^2 (y^2 - 2y)^2 = (y^2 - 2y)(y^2 - 2y)

To expand this, we'll use the FOIL method (First, Outer, Inner, Last): (y^2 - 2y)(y^2 - 2y) = y^2 * y^2 + y^2 * (-2y) - 2y * y^2 + (-2y) * (-2y) = y^4 - 2y^3 - 2y^3 + 4y^2 = y^4 - 4y^3 + 4y^2

Step 2: Expand the second term y^2(y + 3)(y - 3)

To expand this, we'll again use the FOIL method: y^2(y + 3)(y - 3) = y^2 * (y^2 - 3y + 3y - 9) = y^2 * (y^2 - 9) = y^4 - 9y^2

Step 3: Expand the third term 2y(2y^2 + 5) 2y(2y^2 + 5) = 2y * 2y^2 + 2y * 5 = 4y^3 + 10y

Now, let's put all the simplified terms together:

(y^2 - 2y)^2 - y^2(y + 3)(y - 3) + 2y(2y^2 + 5) = (y^4 - 4y^3 + 4y^2) - (y^4 - 9y^2) + (4y^3 + 10y)

Now, combine like terms:

= y^4 - 4y^3 + 4y^2 - y^4 + 9y^2 + 4y^3 + 10y

The terms y^4 and -y^4 cancel each other out, and the terms 4y^3 and -4y^3 also cancel out:

= 9y^2 + 9y^2 + 10y

Finally, combine like terms once more:

= 18y^2 + 10y

So the simplified expression is 18y^2 + 10y.