Question

28. выражение 1)(x-4)²-6 2)10a+(a-5)² 3)(3m-7n)²-9m(n-5n) 4)(6a-3b)²+(9a+2b)² 5)b(b--4)² 6)(12a-b)²-(9a-b)(16a+2b) 7)x(2x-9)²-2x (15+x)² 8)(x+2)²-(x-3)(x+3) 9)(7a-5b)(7a++7b)² 10)(y-2)(y+-1)²+(5-y)(y+5)

Answer 1

1) (x-4)²-6 = x² - 8x + 16 - 6 = x² - 8x + 10

2) 10a+(a-5)² = 10a+a² - 10a + 25 = a² + 25

3 )(3m-7n)²-9m(n-5n) = 9m² - 42 mn + 49n² - 9m(-4n) = 9m² - 42 mn + 49n² + 36mn = 9m² - 6 mn + 49n²

4)(6a-3b)²+(9a+2b)² = 36a² - 36ab + 9b² + 81a² + 36ab + 4b² = 117a² + 13b²

5) b(b-3)-(b-4)² = b²- 3b - b² + 8b - 16 = 5b - 16

6)(12a-b)²-(9a-b)(16a+2b) = 144a² - 24ab + b² - 144a² - 2ab + 2b² = -26ab + 3b²

7)x(2x-9)²-2x (15+x)² = x(4x² - 36x + 81) - 2x(225 + 30x + x²) = 4x³ - 36x² + 81x - 450x - 60x² - 2x³ = 2x³- 96x² - 369x

8) (x+2)²-(x-3)(x+3) = x² + 4x + 4 - x² + 9 = 4x + 13

9) (7a-5b)(7a+5b)-(4a+7b)² = 49a² - 25b² - 16a² - 56ab - 49b² = 33a² - 74b² - 56ab

10) (y-2)(y+3)-(y-1)²+(5-y)(y+5) = y² + y - 6 - y² + 2y - 1 +25 - y² = 3y + 18 - y²

Answer 2

▪1)

${(x - 4)}^{2} - 6 = {x}^{2} - 8x + 16 - 6 = {x}^{2} - 8x + 10$

▪2)

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

▪3)

${(3m - 7n)}^{2} - 9m(n - 5n) = 9 {m}^{2} - 42mn + 49 {n}^{2} - 9mn + 45mn = 9 {m}^{2} - 6mn + 49 {n}^{2}$

▪4)

${(6a - 3b)}^{2} + {(9a + 2b)}^{2} = 36 {a}^{2} - 36ab + 9 {b}^{2} + 81 {a}^{2} + 36ab + 4 {b}^{2} = 117 {a}^{2} + 13 {b}^{2}$

▪5)

$b(b - 3) - {(b - 4)}^{2} = {b}^{2} - 3b - {b}^{2} + 8b - 16 = 5b - 16$

▪6)

${(12a - b)}^{2} - (9a - b)(16a + 2b) = 144 {a}^{2} - 24ab + {b}^{2} - 144 {a}^{2} - 18ab + 16ab + 2 {b}^{2} = - 26ab + 3 {b}^{2}$

▪7)

$x(2x - 9) ^{2} - 2x {(15 + x)}^{2} = x(4 {x}^{2} - 36x + 81) - 2x(225 + 30x + {x}^{2} ) = 4 {x}^{3} - 36 {x}^{2} + 81x - 450x - 60 {x}^{2} - 2 {x}^{3} = 2 {x}^{3} - 96 {x}^{2} - 369x$

▪8)

${(x + 2)}^{2} - (x - 3)(x + 3) = {x}^{2} + 4x + 4 - {x}^{2} + 9 = 4x + 13$

▪9)

$(7a - 5b)(7a + 5b) - (4a + 7b) ^{2} = 49 {a}^{2} - 25 {b}^{2} - 16 {a}^{2} - 56ab - 49 {b}^{2} = 33 {a}^{2} - 74 {b}^{2} - 56ab$

▪10)

$(y - 2)(y + 3) - {(y - 1)}^{2} + (5 - y)(y + 5) = {y}^{2} + 3y - 2y - 6 - {y}^{2} + 2y - 1 + 25 - {y}^{2} = - {y}^{2} + 3y + 18$