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Simplifying (4p + -3q)(9p + 2q) = 36p2 + -19pq + -6q2 Multiply (4p + -3q) * (9p + 2q) (4p * (9p + 2q) + -3q * (9p + 2q)) = 36p2 + -19pq + -6q2 ((9p * 4p + 2q * 4p) + -3q * (9p + 2q)) = 36p2 + -19pq + -6q2 Reorder the terms: ((8pq + 36p2) + -3q * (9p + 2q)) = 36p2 + -19pq + -6q2 ((8pq + 36p2) + -3q * (9p + 2q)) = 36p2 + -19pq + -6q2 (8pq + 36p2 + (9p * -3q + 2q * -3q)) = 36p2 + -19pq + -6q2 (8pq + 36p2 + (-27pq + -6q2)) = 36p2 + -19pq + -6q2 Reorder the terms: (8pq + -27pq + 36p2 + -6q2) = 36p2 + -19pq + -6q2 Combine like terms: 8pq + -27pq = -19pq (-19pq + 36p2 + -6q2) = 36p2 + -19pq + -6q2 Reorder the terms: -19pq + 36p2 + -6q2 = -19pq + 36p2 + -6q2 Add '19pq' to each side of the equation. -19pq + 36p2 + 19pq + -6q2 = -19pq + 36p2 + 19pq + -6q2 Reorder the terms: -19pq + 19pq + 36p2 + -6q2 = -19pq + 36p2 + 19pq + -6q2 Combine like terms: -19pq + 19pq = 0 0 + 36p2 + -6q2 = -19pq + 36p2 + 19pq + -6q2 36p2 + -6q2 = -19pq + 36p2 + 19pq + -6q2 Reorder the terms: 36p2 + -6q2 = -19pq + 19pq + 36p2 + -6q2 Combine like terms: -19pq + 19pq = 0 36p2 + -6q2 = 0 + 36p2 + -6q2 36p2 + -6q2 = 36p2 + -6q2 Add '-36p2' to each side of the equation. 36p2 + -36p2 + -6q2 = 36p2 + -36p2 + -6q2 Combine like terms: 36p2 + -36p2 = 0 0 + -6q2 = 36p2 + -36p2 + -6q2 -6q2 = 36p2 + -36p2 + -6q2 Combine like terms: 36p2 + -36p2 = 0 -6q2 = 0 + -6q2 -6q2 = -6q2 Add '6q2' to each side of the equation. -6q2 + 6q2 = -6q2 + 6q2 Combine like terms: -6q2 + 6q2 = 0 0 = -6q2 + 6q2 Combine like terms: -6q2 + 6q2 = 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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