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Simplifying f(x) = X(x + 2)(x + -2)(x2 + -4) Multiply f * x fx = X(x + 2)(x + -2)(x2 + -4) Reorder the terms: fx = X(2 + x)(x + -2)(x2 + -4) Reorder the terms: fx = X(2 + x)(-2 + x)(x2 + -4) Reorder the terms: fx = X(2 + x)(-2 + x)(-4 + x2) Multiply (2 + x) * (-2 + x) fx = X(2(-2 + x) + x(-2 + x))(-4 + x2) fx = X((-2 * 2 + x * 2) + x(-2 + x))(-4 + x2) fx = X((-4 + 2x) + x(-2 + x))(-4 + x2) fx = X(-4 + 2x + (-2 * x + x * x))(-4 + x2) fx = X(-4 + 2x + (-2x + x2))(-4 + x2) Combine like terms: 2x + -2x = 0 fx = X(-4 + 0 + x2)(-4 + x2) fx = X(-4 + x2)(-4 + x2) Multiply (-4 + x2) * (-4 + x2) fx = X(-4(-4 + x2) + x2(-4 + x2)) fx = X((-4 * -4 + x2 * -4) + x2(-4 + x2)) fx = X((16 + -4x2) + x2(-4 + x2)) fx = X(16 + -4x2 + (-4 * x2 + x2 * x2)) fx = X(16 + -4x2 + (-4x2 + x4)) Combine like terms: -4x2 + -4x2 = -8x2 fx = X(16 + -8x2 + x4) fx = (16 * X + -8x2 * X + x4 * X) fx = (16X + -8x2X + x4X) Solving fx = 16X + -8x2X + x4X Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = 16x-1X + -8xX + x3X Simplifying f = 16x-1X + -8xX + x3X
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