Question

3

6

4 (1)

1 (3)

2 (3,4)

Answer 1

3.

$(9 - {b}^{2} )(9 + {b}^{2} ) + {(4 + {b}^{2}) }^{2} = 81 - {b}^{4} + 16 + 8 {b}^{2} + {b}^{4} = 97 + 8 {b}^{2}$

если b = 1/2, то:

$97 + 8 \times {( \frac{1}{2} )}^{2} = 97 + 8 \times \frac{1}{4} = 97 + \frac{8}{4} = 97 + 2 = 99$

4(1).

$4(9 {y}^{2} + 6y + 1) - 27 = 16 {y}^{2} - 81 + 2(10 {y}^{2} - 35y + 4y - 14) \\ 36 {y}^{2} + 24y + 4 - 27 = 16 {y}^{2} - 81 + 20 {y}^{2} - 70y + 8y - 28 \\ 36 {y}^{2} - 16 {y}^{2} - 20 {y}^{2} + 24y + 70y - 8y = - 4 + 27 - 81 - 28 \\ 86y = - 86 \\ y = \frac{ - 86}{86} \\ y = - 1$

1(3).

$9 {p}^{8} + 30 {p}^{4} {k}^{6} + 25 {k}^{12}$

2(3).

$36 {b}^{6} - 96 {b}^{3} {c}^{7} + 64 {c}^{14} = {(6 {b}^{3} - 8 {c}^{7} )}^{2} = (6 {b}^{3} - 8 {c}^{7} )(6 {b}^{3} - 8 {c}^{7} )$

2(4).

${49}^{n} - 2 \times {28}^{n} + {16}^{n} = {(7 - 4)}^{2n}$

6.

25=(a+b-c)²=a²+b²+c²+2(ab-bc-ac) » a²+b²+c²=25-2(-2)=25+4=29