3. Expand and simplify. a) (4m + 1)(3m 2) + 2(2m 1)(–3m + 4) – – b) (6h + 2)(2h 3) (4h 3k)2 k – – – – Solution Use the order of operations. Multiply before adding and subtracting. Then combine like terms. (4m + 1)(3m 2) + 2(2m 1)(–3m + 4) a) – – = 4m(3m 2) + 1(3m 2) + 2[(2m(–3m + 4) 1(–3m + 4)] – – – = 12m2 8m + 3m 2 + 2[–6m2 + 8m + 3m 4] – – – = 12m2 5m 2 + 2[–6m2 + 11m 4] – – – = 12m2 5m 2 12m2 + 22m 8 – – – – = 17m 10 – (6h + 2)(2h 3) (4h 3k)2 b) k – – – – = 6h(2h 3) + 3) 2(2h 3) (4h 3k)(4h 3k) k(2h – – – – – – – = 12h2 18h + 2hk 3k 4h + 6 [4h(4h 3k) 3k(4h 3k)] – – – – – – – = 12h2 22h + 2hk 3k + 6 [16h2 12hk 12hk + 9k2] – – – – – = 12h2 22h + 2hk 3k + 6 (16h2 24hk + 9k2) – – – – = 12h2 22h + 2hk 3k + 6 16h2 + 24hk 9k2 – – – – = 22h + 26hk 3k + 6 9k2 –4h2 – – – Homework page 186 #4-5 #6a, 7, 9-12, 14-15, 17 #21-22
3. Expand and simplify. a) (4m + 1)(3m – 2) + 2(2m – 1)(–3m + 4) b) (6h + k – 2)(2h – 3) – (4h – 3k)2 Solution Use the order of operations. Multiply before adding and subtracting. Then combine like terms. a) (4m + 1)(3m – 2) + 2(2m – 1)(–3m + 4) = 4m(3m – 2) + 1(3m – 2) + 2[(2m(–3m + 4) – 1(–3m + 4)] = 12m2 – 8m + 3m – 2 + 2[–6m2 + 8m + 3m – 4] = 12m2 – 5m – 2 + 2[–6m2 + 11m – 4] = 12m2 – 5m – 2 – 12m2 + 22m – 8 = 17m – 10 b) (6h + k – 2)(2h – 3) – (4h – 3k)2 = 6h(2h – 3) + k(2h – 3) – 2(2h – 3) – (4h – 3k)(4h – 3k) = 12h2 – 18h + 2hk – 3k – 4h + 6 – [4h(4h – 3k) – 3k(4h – 3k)] = 12h2 – 22h + 2hk – 3k + 6 – [16h2 – 12hk – 12hk + 9k2] = 12h2 – 22h + 2hk – 3k + 6 – (16h2 – 24hk + 9k2) = 12h2 – 22h + 2hk – 3k + 6 – 16h2 + 24hk – 9k2 = –4h2 – 22h + 26hk – 3k + 6 – 9k2 Homework page 186 #4-5 #6a, 7, 9-12, 14-15, 17 #21-22
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