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Simplifying (2a + -3b)(4a2 + 6ab + 9b2) + 27b3 = 8a3 Reorder the terms: (2a + -3b)(6ab + 4a2 + 9b2) + 27b3 = 8a3 Multiply (2a + -3b) * (6ab + 4a2 + 9b2) (2a * (6ab + 4a2 + 9b2) + -3b * (6ab + 4a2 + 9b2)) + 27b3 = 8a3 ((6ab * 2a + 4a2 * 2a + 9b2 * 2a) + -3b * (6ab + 4a2 + 9b2)) + 27b3 = 8a3 Reorder the terms: ((18ab2 + 12a2b + 8a3) + -3b * (6ab + 4a2 + 9b2)) + 27b3 = 8a3 ((18ab2 + 12a2b + 8a3) + -3b * (6ab + 4a2 + 9b2)) + 27b3 = 8a3 (18ab2 + 12a2b + 8a3 + (6ab * -3b + 4a2 * -3b + 9b2 * -3b)) + 27b3 = 8a3 (18ab2 + 12a2b + 8a3 + (-18ab2 + -12a2b + -27b3)) + 27b3 = 8a3 Reorder the terms: (18ab2 + -18ab2 + 12a2b + -12a2b + 8a3 + -27b3) + 27b3 = 8a3 Combine like terms: 18ab2 + -18ab2 = 0 (0 + 12a2b + -12a2b + 8a3 + -27b3) + 27b3 = 8a3 (12a2b + -12a2b + 8a3 + -27b3) + 27b3 = 8a3 Combine like terms: 12a2b + -12a2b = 0 (0 + 8a3 + -27b3) + 27b3 = 8a3 (8a3 + -27b3) + 27b3 = 8a3 Combine like terms: -27b3 + 27b3 = 0 8a3 + 0 = 8a3 8a3 = 8a3 Add '-8a3' to each side of the equation. 8a3 + -8a3 = 8a3 + -8a3 Combine like terms: 8a3 + -8a3 = 0 0 = 8a3 + -8a3 Combine like terms: 8a3 + -8a3 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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