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Simplifying 2tu(t + -4) = 2(t + -4) * u(t + -4) + 8u(t + -4) Reorder the terms: 2tu(-4 + t) = 2(t + -4) * u(t + -4) + 8u(t + -4) (-4 * 2tu + t * 2tu) = 2(t + -4) * u(t + -4) + 8u(t + -4) (-8tu + 2t2u) = 2(t + -4) * u(t + -4) + 8u(t + -4) Reorder the terms: -8tu + 2t2u = 2(-4 + t) * u(t + -4) + 8u(t + -4) Reorder the terms: -8tu + 2t2u = 2(-4 + t) * u(-4 + t) + 8u(t + -4) Reorder the terms for easier multiplication: -8tu + 2t2u = 2u(-4 + t)(-4 + t) + 8u(t + -4) Multiply (-4 + t) * (-4 + t) -8tu + 2t2u = 2u(-4(-4 + t) + t(-4 + t)) + 8u(t + -4) -8tu + 2t2u = 2u((-4 * -4 + t * -4) + t(-4 + t)) + 8u(t + -4) -8tu + 2t2u = 2u((16 + -4t) + t(-4 + t)) + 8u(t + -4) -8tu + 2t2u = 2u(16 + -4t + (-4 * t + t * t)) + 8u(t + -4) -8tu + 2t2u = 2u(16 + -4t + (-4t + t2)) + 8u(t + -4) Combine like terms: -4t + -4t = -8t -8tu + 2t2u = 2u(16 + -8t + t2) + 8u(t + -4) -8tu + 2t2u = (16 * 2u + -8t * 2u + t2 * 2u) + 8u(t + -4) Reorder the terms: -8tu + 2t2u = (-16tu + 2t2u + 32u) + 8u(t + -4) -8tu + 2t2u = (-16tu + 2t2u + 32u) + 8u(t + -4) Reorder the terms: -8tu + 2t2u = -16tu + 2t2u + 32u + 8u(-4 + t) -8tu + 2t2u = -16tu + 2t2u + 32u + (-4 * 8u + t * 8u) Reorder the terms: -8tu + 2t2u = -16tu + 2t2u + 32u + (8tu + -32u) -8tu + 2t2u = -16tu + 2t2u + 32u + (8tu + -32u) Reorder the terms: -8tu + 2t2u = -16tu + 8tu + 2t2u + 32u + -32u Combine like terms: -16tu + 8tu = -8tu -8tu + 2t2u = -8tu + 2t2u + 32u + -32u Combine like terms: 32u + -32u = 0 -8tu + 2t2u = -8tu + 2t2u + 0 -8tu + 2t2u = -8tu + 2t2u Add '8tu' to each side of the equation. -8tu + 8tu + 2t2u = -8tu + 8tu + 2t2u Combine like terms: -8tu + 8tu = 0 0 + 2t2u = -8tu + 8tu + 2t2u 2t2u = -8tu + 8tu + 2t2u Combine like terms: -8tu + 8tu = 0 2t2u = 0 + 2t2u 2t2u = 2t2u Add '-2t2u' to each side of the equation. 2t2u + -2t2u = 2t2u + -2t2u Combine like terms: 2t2u + -2t2u = 0 0 = 2t2u + -2t2u Combine like terms: 2t2u + -2t2u = 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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