Question

добрый вечер , решите пожалуйста все задания, 22 балла за правильный ответ

Answer 1

1)

$(x + 4) {}^{2} = {x}^{2} + 8x + 16$

$(y - 5x) {}^{2} = {y}^{2} - 10x + 25x {}^{2}$

$(3a - 2)(3a + 2) = 9a {}^{2} - 4$

$(c - 2b)(c + 2b) = c {}^{2} - 4b {}^{2}$

2)

${x}^{2} - 81 = (x - 9)(x + 9)$

${y}^{2} - 4y + 4 = ( y - 2) {}^{2}$

3)

$(c + 6) {}^{2} - c(c + 12) = c {}^{2} + 12 c + 36- c {}^{2} - 12 c = 36$

4)

${(x + 7)}^{2} - (x - 4)(x + 4) = 65 \\ {x}^{2} + 14x + 49 - {x}^{2} + 16 = 65 \\ 14x = 0 \\ x = 0$

$y {}^{2} - \frac{49}{64} = 0 \\ {y}^{2} = \frac{49}{64} \\ y = \frac{7}{8} \\ y = - \frac{7}{8}$

5)

$(4a { }^{2} + b {}^{2} )(2a + b)(2a - b) = (4a { }^{2} + b {}^{2} )(4a { }^{2} - b {}^{2} ) = 16 {a}^{4} - b {}^{4}$

$\frac{1}{2} (2m + 4n)(m - 2n) = \frac{1}{2} (2(m + 2n))(m - 2n) = 1 \times (m + 2n)(m - 2n) = {m}^{2} - 4 {n}^{2}$

6)

$36 {x}^{4} {y}^{2} - 169c {}^{4} = (6 {x}^{2} y - 13c {}^{2} )(6 {x}^{2} y + 13c {}^{2} )$

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