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Simplifying (2a + -3b)(4a2 + 6ab + 9b2) + 27b2 = 8a3 Reorder the terms: (2a + -3b)(6ab + 4a2 + 9b2) + 27b2 = 8a3 Multiply (2a + -3b) * (6ab + 4a2 + 9b2) (2a * (6ab + 4a2 + 9b2) + -3b * (6ab + 4a2 + 9b2)) + 27b2 = 8a3 ((6ab * 2a + 4a2 * 2a + 9b2 * 2a) + -3b * (6ab + 4a2 + 9b2)) + 27b2 = 8a3 Reorder the terms: ((18ab2 + 12a2b + 8a3) + -3b * (6ab + 4a2 + 9b2)) + 27b2 = 8a3 ((18ab2 + 12a2b + 8a3) + -3b * (6ab + 4a2 + 9b2)) + 27b2 = 8a3 (18ab2 + 12a2b + 8a3 + (6ab * -3b + 4a2 * -3b + 9b2 * -3b)) + 27b2 = 8a3 (18ab2 + 12a2b + 8a3 + (-18ab2 + -12a2b + -27b3)) + 27b2 = 8a3 Reorder the terms: (18ab2 + -18ab2 + 12a2b + -12a2b + 8a3 + -27b3) + 27b2 = 8a3 Combine like terms: 18ab2 + -18ab2 = 0 (0 + 12a2b + -12a2b + 8a3 + -27b3) + 27b2 = 8a3 (12a2b + -12a2b + 8a3 + -27b3) + 27b2 = 8a3 Combine like terms: 12a2b + -12a2b = 0 (0 + 8a3 + -27b3) + 27b2 = 8a3 (8a3 + -27b3) + 27b2 = 8a3 Reorder the terms: 8a3 + 27b2 + -27b3 = 8a3 Add '-8a3' to each side of the equation. 8a3 + 27b2 + -8a3 + -27b3 = 8a3 + -8a3 Reorder the terms: 8a3 + -8a3 + 27b2 + -27b3 = 8a3 + -8a3 Combine like terms: 8a3 + -8a3 = 0 0 + 27b2 + -27b3 = 8a3 + -8a3 27b2 + -27b3 = 8a3 + -8a3 Combine like terms: 8a3 + -8a3 = 0 27b2 + -27b3 = 0 Solving 27b2 + -27b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '27b2'. 27b2(1 + -1b) = 0 Ignore the factor 27.Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2 = 0 Take the square root of each side: b = {0}Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1Solution
b = {0, 1}
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