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Simplifying (1 + 3w + w2)(1 + w + 2w2) = 2 Multiply (1 + 3w + w2) * (1 + w + 2w2) (1(1 + w + 2w2) + 3w * (1 + w + 2w2) + w2(1 + w + 2w2)) = 2 ((1 * 1 + w * 1 + 2w2 * 1) + 3w * (1 + w + 2w2) + w2(1 + w + 2w2)) = 2 ((1 + 1w + 2w2) + 3w * (1 + w + 2w2) + w2(1 + w + 2w2)) = 2 (1 + 1w + 2w2 + (1 * 3w + w * 3w + 2w2 * 3w) + w2(1 + w + 2w2)) = 2 (1 + 1w + 2w2 + (3w + 3w2 + 6w3) + w2(1 + w + 2w2)) = 2 (1 + 1w + 2w2 + 3w + 3w2 + 6w3 + (1 * w2 + w * w2 + 2w2 * w2)) = 2 (1 + 1w + 2w2 + 3w + 3w2 + 6w3 + (1w2 + w3 + 2w4)) = 2 Reorder the terms: (1 + 1w + 3w + 2w2 + 3w2 + 1w2 + 6w3 + w3 + 2w4) = 2 Combine like terms: 1w + 3w = 4w (1 + 4w + 2w2 + 3w2 + 1w2 + 6w3 + w3 + 2w4) = 2 Combine like terms: 2w2 + 3w2 = 5w2 (1 + 4w + 5w2 + 1w2 + 6w3 + w3 + 2w4) = 2 Combine like terms: 5w2 + 1w2 = 6w2 (1 + 4w + 6w2 + 6w3 + w3 + 2w4) = 2 Combine like terms: 6w3 + w3 = 7w3 (1 + 4w + 6w2 + 7w3 + 2w4) = 2 Solving 1 + 4w + 6w2 + 7w3 + 2w4 = 2 Solving for variable 'w'. Reorder the terms: 1 + -2 + 4w + 6w2 + 7w3 + 2w4 = 2 + -2 Combine like terms: 1 + -2 = -1 -1 + 4w + 6w2 + 7w3 + 2w4 = 2 + -2 Combine like terms: 2 + -2 = 0 -1 + 4w + 6w2 + 7w3 + 2w4 = 0 The solution to this equation could not be determined.
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