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Simplifying y = [x + 1][x + 1][x + -1(-2 + -2i)][x + -1(-2 + 2i)] Reorder the terms: y = [1 + x][x + 1][x + -1(-2 + -2i)][x + -1(-2 + 2i)] Reorder the terms: y = [1 + x][1 + x][x + -1(-2 + -2i)][x + -1(-2 + 2i)] y = [1 + x][1 + x][x + (-2 * -1 + -2i * -1)][x + -1(-2 + 2i)] y = [1 + x][1 + x][x + (2 + 2i)][x + -1(-2 + 2i)] Reorder the terms: y = [1 + x][1 + x][2 + 2i + x][x + -1(-2 + 2i)] y = [1 + x][1 + x][2 + 2i + x][x + (-2 * -1 + 2i * -1)] y = [1 + x][1 + x][2 + 2i + x][x + (2 + -2i)] Reorder the terms: y = [1 + x][1 + x][2 + 2i + x][2 + -2i + x] Multiply [1 + x] * [1 + x] y = [1[1 + x] + x[1 + x]][2 + 2i + x][2 + -2i + x] y = [[1 * 1 + x * 1] + x[1 + x]][2 + 2i + x][2 + -2i + x] y = [[1 + 1x] + x[1 + x]][2 + 2i + x][2 + -2i + x] y = [1 + 1x + [1 * x + x * x]][2 + 2i + x][2 + -2i + x] y = [1 + 1x + [1x + x2]][2 + 2i + x][2 + -2i + x] Combine like terms: 1x + 1x = 2x y = [1 + 2x + x2][2 + 2i + x][2 + -2i + x] Multiply [1 + 2x + x2] * [2 + 2i + x] y = [1[2 + 2i + x] + 2x * [2 + 2i + x] + x2[2 + 2i + x]][2 + -2i + x] y = [[2 * 1 + 2i * 1 + x * 1] + 2x * [2 + 2i + x] + x2[2 + 2i + x]][2 + -2i + x] y = [[2 + 2i + 1x] + 2x * [2 + 2i + x] + x2[2 + 2i + x]][2 + -2i + x] y = [2 + 2i + 1x + [2 * 2x + 2i * 2x + x * 2x] + x2[2 + 2i + x]][2 + -2i + x] Reorder the terms: y = [2 + 2i + 1x + [4ix + 4x + 2x2] + x2[2 + 2i + x]][2 + -2i + x] y = [2 + 2i + 1x + [4ix + 4x + 2x2] + x2[2 + 2i + x]][2 + -2i + x] y = [2 + 2i + 1x + 4ix + 4x + 2x2 + [2 * x2 + 2i * x2 + x * x2]][2 + -2i + x] Reorder the terms: y = [2 + 2i + 1x + 4ix + 4x + 2x2 + [2ix2 + 2x2 + x3]][2 + -2i + x] y = [2 + 2i + 1x + 4ix + 4x + 2x2 + [2ix2 + 2x2 + x3]][2 + -2i + x] Reorder the terms: y = [2 + 2i + 4ix + 2ix2 + 1x + 4x + 2x2 + 2x2 + x3][2 + -2i + x] Combine like terms: 1x + 4x = 5x y = [2 + 2i + 4ix + 2ix2 + 5x + 2x2 + 2x2 + x3][2 + -2i + x] Combine like terms: 2x2 + 2x2 = 4x2 y = [2 + 2i + 4ix + 2ix2 + 5x + 4x2 + x3][2 + -2i + x] Multiply [2 + 2i + 4ix + 2ix2 + 5x + 4x2 + x3] * [2 + -2i + x] y = [2[2 + -2i + x] + 2i * [2 + -2i + x] + 4ix * [2 + -2i + x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [[2 * 2 + -2i * 2 + x * 2] + 2i * [2 + -2i + x] + 4ix * [2 + -2i + x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [[4 + -4i + 2x] + 2i * [2 + -2i + x] + 4ix * [2 + -2i + x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + [2 * 2i + -2i * 2i + x * 2i] + 4ix * [2 + -2i + x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] Reorder the terms: y = [4 + -4i + 2x + [4i + 2ix + -4i2] + 4ix * [2 + -2i + x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + [4i + 2ix + -4i2] + 4ix * [2 + -2i + x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + [2 * 4ix + -2i * 4ix + x * 4ix] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] Reorder the terms: y = [4 + -4i + 2x + 4i + 2ix + -4i2 + [8ix + 4ix2 + -8i2x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + [8ix + 4ix2 + -8i2x] + 2ix2 * [2 + -2i + x] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + [2 * 2ix2 + -2i * 2ix2 + x * 2ix2] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] Reorder the terms: y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + [4ix2 + 2ix3 + -4i2x2] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + [4ix2 + 2ix3 + -4i2x2] + 5x * [2 + -2i + x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + [2 * 5x + -2i * 5x + x * 5x] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] Reorder the terms: y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + [-10ix + 10x + 5x2] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + [-10ix + 10x + 5x2] + 4x2 * [2 + -2i + x] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + -10ix + 10x + 5x2 + [2 * 4x2 + -2i * 4x2 + x * 4x2] + x3[2 + -2i + x]] Reorder the terms: y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + -10ix + 10x + 5x2 + [-8ix2 + 8x2 + 4x3] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + -10ix + 10x + 5x2 + [-8ix2 + 8x2 + 4x3] + x3[2 + -2i + x]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + -10ix + 10x + 5x2 + -8ix2 + 8x2 + 4x3 + [2 * x3 + -2i * x3 + x * x3]] Reorder the terms: y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + -10ix + 10x + 5x2 + -8ix2 + 8x2 + 4x3 + [-2ix3 + 2x3 + x4]] y = [4 + -4i + 2x + 4i + 2ix + -4i2 + 8ix + 4ix2 + -8i2x + 4ix2 + 2ix3 + -4i2x2 + -10ix + 10x + 5x2 + -8ix2 + 8x2 + 4x3 + [-2ix3 + 2x3 + x4]] Reorder the terms: y = [4 + -4i + 4i + 2ix + 8ix + -10ix + 4ix2 + 4ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: -4i + 4i = 0 y = [4 + 0 + 2ix + 8ix + -10ix + 4ix2 + 4ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] y = [4 + 2ix + 8ix + -10ix + 4ix2 + 4ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 2ix + 8ix = 10ix y = [4 + 10ix + -10ix + 4ix2 + 4ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 10ix + -10ix = 0 y = [4 + 0 + 4ix2 + 4ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] y = [4 + 4ix2 + 4ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 4ix2 + 4ix2 = 8ix2 y = [4 + 8ix2 + -8ix2 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 8ix2 + -8ix2 = 0 y = [4 + 0 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] y = [4 + 2ix3 + -2ix3 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 2ix3 + -2ix3 = 0 y = [4 + 0 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] y = [4 + -4i2 + -8i2x + -4i2x2 + 2x + 10x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 2x + 10x = 12x y = [4 + -4i2 + -8i2x + -4i2x2 + 12x + 5x2 + 8x2 + 4x3 + 2x3 + x4] Combine like terms: 5x2 + 8x2 = 13x2 y = [4 + -4i2 + -8i2x + -4i2x2 + 12x + 13x2 + 4x3 + 2x3 + x4] Combine like terms: 4x3 + 2x3 = 6x3 y = [4 + -4i2 + -8i2x + -4i2x2 + 12x + 13x2 + 6x3 + x4] Solving y = 4 + -4i2 + -8i2x + -4i2x2 + 12x + 13x2 + 6x3 + x4 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 4 + -4i2 + -8i2x + -4i2x2 + 12x + 13x2 + 6x3 + x4
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