( ?)(8y^2−4y^4)=40y^4−20y^6
In order to verify if the given equation is correct, let's simplify the left side of the equation step by step:
8y^2 - 4y^4
Factor out a common factor of 4y^2:
4y^2(2 - y^2)
Factor out a common factor of -1 in the parentheses:
4y^2(-1)(y^2 - 2)
Rearrange the terms:
-4y^2(y^2 - 2)
Now multiply the terms inside the parentheses:
-4y^2(y^2) + 4y^2(2)
-4y^4 + 8y^2
Therefore, 8y^2 - 4y^4 simplifies to -4y^4 + 8y^2.
Given equation: -4y^4 + 8y^2 = 40y^4 - 20y^6
This means that -4y^4 + 8y^2 is not equal to 40y^4 - 20y^6. The given equation is not correct.