8 (x-2)(x^2-1)=(4x^2-2x+1)(2x+1)

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вопрос

Let's first expand the left side of the equation:

(x-2)(x^2-1)
= x(x^2) - x(1) - 2(x^2) + 2(1)
= x^3 - x - 2x^2 + 2

Now, let's expand the right side of the equation:

(4x^2 - 2x + 1)(2x + 1)
= 4x^2(2x) + 4x^2(1) - 2x(2x) - 2x(1) + 1(2x) + 1(1)
= 8x^3 + 4x^2 - 4x^2 - 2x + 2x + 1
= 8x^3 + 1

Therefore, the original equation becomes:

x^3 - x - 2x^2 + 2 = 8x^3 + 1

Now, let's simplify the equation further:

x^3 - x - 2x^2 + 2 = 8x^3 + 1
=> - x - 2x^2 + 2 = 7x^3 + 1
=> 0 = 8x^3 + x^2 + x - 1

Thus, the simplified equation is 8x^3 + x^2 + x - 1 = 0.