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Simplifying h(t) = a(t + 5)(t2 + 9) Multiply h * t ht = a(t + 5)(t2 + 9) Reorder the terms: ht = a(5 + t)(t2 + 9) Reorder the terms: ht = a(5 + t)(9 + t2) Multiply (5 + t) * (9 + t2) ht = a(5(9 + t2) + t(9 + t2)) ht = a((9 * 5 + t2 * 5) + t(9 + t2)) ht = a((45 + 5t2) + t(9 + t2)) ht = a(45 + 5t2 + (9 * t + t2 * t)) ht = a(45 + 5t2 + (9t + t3)) Reorder the terms: ht = a(45 + 9t + 5t2 + t3) ht = a(45 + 9t + 5t2 + t3) ht = (45 * a + 9t * a + 5t2 * a + t3 * a) ht = (45a + 9at + 5at2 + at3) Solving ht = 45a + 9at + 5at2 + at3 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Divide each side by 't'. h = 45at-1 + 9a + 5at + at2 Simplifying h = 45at-1 + 9a + 5at + at2 Reorder the terms: h = 9a + 45at-1 + 5at + at2
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