Let's expand the left side of the equation to prove that it is equal to the right side.
(8x^2 - 3x + 1)^2
= (8x^2 - 3x + 1)(8x^2 - 3x + 1)= 8x^2(8x^2) + 8x^2(-3x) + 8x^2(1) - 3x(8x^2) - 3x(-3x) - 3x(1) + 1(8x^2) + 1(-3x) + 1(1)= 64x^4 - 24x^3 + 8x^2 - 24x^3 + 9x^2 - 3x + 8x^2 - 3x + 1= 64x^4 - 48x^3 + 26x^2 - 6x + 1
Therefore, (8x^2 - 3x + 1)^2 = 64x^4 - 48x^3 + 26x^2 - 6x + 1
Since we know that 64x^4 - 48x^3 + 26x^2 - 6x + 1 is equivalent to 32x^2 - 12x + 1, we have proven that the left side of the equation is indeed equal to the right side.
Let's expand the left side of the equation to prove that it is equal to the right side.
(8x^2 - 3x + 1)^2
= (8x^2 - 3x + 1)(8x^2 - 3x + 1)
= 8x^2(8x^2) + 8x^2(-3x) + 8x^2(1) - 3x(8x^2) - 3x(-3x) - 3x(1) + 1(8x^2) + 1(-3x) + 1(1)
= 64x^4 - 24x^3 + 8x^2 - 24x^3 + 9x^2 - 3x + 8x^2 - 3x + 1
= 64x^4 - 48x^3 + 26x^2 - 6x + 1
Therefore, (8x^2 - 3x + 1)^2 = 64x^4 - 48x^3 + 26x^2 - 6x + 1
Since we know that 64x^4 - 48x^3 + 26x^2 - 6x + 1 is equivalent to 32x^2 - 12x + 1, we have proven that the left side of the equation is indeed equal to the right side.