Question

5.3. Преобразуйте выражение

помогите пж дам 50 балла​

Answer 1

1)

$(x - \frac{1}{2} ) ^{2} = {x}^{2} - 2x \frac{1}{2} + (\frac{1}{2} ) ^{2} = {x}^{2} - x + \frac{1}{4}$

2)

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

3)

$(a - \frac{1}{5} )^{2} = a^{2} - 2a \frac{1}{5} + ( \frac{1}{5} )^{2} = a^{2} - \frac{2}{5} a + \frac{1}{25}$

4) (не уверена)

$( \frac{a}{2} + \frac{b}{3} ) ^{2} = ( \frac{1}{6} (3a + 2b))^{2} = \frac{1}{36} (3a + 2b) ^{2} = \frac{1}{36} (3a ^{2} + 2 \times 3a \times 2b + 2b^{2} ) = \frac{1}{36} (9a ^{2} + 12ab + 4b ^{2} )$

5)

$( \frac{x}{4} + \frac{y}{3} )^{2} = \frac{x^{2} }{16} + 2 \times \frac{x}{4} \times \frac{y}{3} + \frac{y ^{2} }{9} = \frac{ {x}^{2} }{16} + \frac{xy}{6} + \frac{ {y}^{2} }{9}$

6)

$(2 \frac{1}{3} m + 1 \frac{1}{2} n) ^{2} = \frac{49}{9} {m}^{2} + 2 \times \frac{7}{3}m \times \frac{3}{2} n + \frac{9}{4} n ^{2} = \frac{49}{9} {m}^{2} + 7mn + \frac{9}{4} {n}^{2}$

7)

$(5m - \frac{n}{2} ) ^{2} = 25 {m}^{2} - \frac{10mn}{2} + \frac{ {n}^{2} }{4} = 25 {m}^{2} - 5mn + \frac{ {n}^{2} }{4}$

8)

$(9p - \frac{q}{3} ) ^{2} = 81p^{2} - \frac{18pq}{3} + \frac{ {q}^{2} }{9} = 81 {p}^{2} - 6pq + \frac{ {q}^{2} }{9}$