First, let's expand each term in the equation:
(x^2 + 2x)^2 = x^4 + 4x^3 + 4x^24(x + 1)^2 = 4(x^2 + 2x + 1) = 4x^2 + 8x + 4
Now, substitute these expressions back into the equation:
(x^4 + 4x^3 + 4x^2) - (4x^2 + 8x + 4) + 7 = 0x^4 + 4x^3 + 4x^2 - 4x^2 - 8x - 4 + 7 = 0x^4 + 4x^3 - 8x + 3 = 0
Therefore, the simplified form of the given equation is x^4 + 4x^3 - 8x + 3 = 0.
First, let's expand each term in the equation:
(x^2 + 2x)^2 = x^4 + 4x^3 + 4x^2
4(x + 1)^2 = 4(x^2 + 2x + 1) = 4x^2 + 8x + 4
Now, substitute these expressions back into the equation:
(x^4 + 4x^3 + 4x^2) - (4x^2 + 8x + 4) + 7 = 0
x^4 + 4x^3 + 4x^2 - 4x^2 - 8x - 4 + 7 = 0
x^4 + 4x^3 - 8x + 3 = 0
Therefore, the simplified form of the given equation is x^4 + 4x^3 - 8x + 3 = 0.