Question

VA ROG AHUTAȚIMA MA EXERCITIUL 8 va dau COROANA SI MULTE PUNCTE
ESTE FOARTE URGENT
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Answer 1

Răspuns:

$8)a) {(7a + 5)}^{2} = 49 {a}^{2} + 2 \times 7a \times 5 + {5}^{2} = 49 {a}^{2} + 70a + 25 \\ {(3b - 5c)}^{2} = 9 {b}^{2} - 2 \times 3b \times 5c + 25 {c}^{2} = {9b}^{2} - 30bc + 25 {c}^{2} \\ (2u + v)(2u - v) = 4 {u}^{2} - {v}^{2}$

$b) {( \frac{1}{2}a + 3) }^{2} = \frac{1}{4} {a}^{2} + 2 \times \frac{1}{2} \times a \times 3 + {3}^{2} = \frac{1}{ {4} } {a}^{2} + 3a + 9 \\ {( \frac{2}{3}x - 3y) }^{2} = \frac{4}{9} {x}^{2} - 2 \times \frac{2}{3} \times x \times 3y + 9 {y}^{2} = \frac{4}{9} {x}^{2} - 4xy + 9 {y}^{2}$

$( \frac{1}{3} a + \frac{1}{2} b)( \frac{1}{3} a - \frac{1}{2} b) = \frac{1}{9} {a}^{2} - \frac{1}{4} {b}^{2}$

$c) {( \sqrt{5} a + 3)}^{2} = 5 {a}^{2} + 2 \times \sqrt{5} a \times 3 + {3}^{2} = 5 {a}^{2} + 6 \sqrt{5} a + 9 \\ {( \sqrt{2}x - \sqrt{3} y) }^{2} = 2 {x}^{2} - 2 \times \sqrt{2} x \times \sqrt{3}y + 3 {y}^{2} = 2 {x}^{2} - 2 \sqrt{6} xy + 3 {y}^{2}$

$( \sqrt{2} p + \sqrt{5} q)( \sqrt{2} p - \sqrt{5} q) = {( \sqrt{2}p) }^{2} - {( \sqrt{5}q) }^{2} = 2 {p}^{2} - 5 {q}^{2}$