Question

Упростите выражение : 1) (11а - b) ² + (9a + 7b)(8a - 13b) 2) (18x + 5y)(2x - 4y) - (6x - 3y)² 3) 4x(3x - 2y) - (10y - 0,4x)² 4) (15a + 2b)² - (3a - 7b)(3b - 5a)

Answer 1

1)

$121 {a}^{2} - 22ab + {b}^{2} + 72 {a}^{2} - 117ab + 56ab - 91 {b}^{2} =193 {a}^{2} - 90 {b}^{2} - 83$

2)

$36 {x}^{2} - 72xy + 10xy - 20 {y}^{2} - 36 {x}^{2} + 36xy - 9 {y}^{2} = - 29 {y}^{2} - 26xy$

3)

$12 {x}^{2} - 8xy - 100 {y}^{2} + 8xy - 0.16 {x}^{2} = 11.84 {x}^{2} - 100 {y}^{2}$

4)

$225 {a}^{2} + 120ab - 9ab + 15 {a}^{2} + 21 {b}^{2} + 15 {a}^{2} = 255 {a}^{2} + 21{b}^{2} + 111ab$

Answer 2

1. (11a - b)² + (9a + 7b)(8a - 13b)

First, let's simplify the square term: (11a - b)² = (11a - b)(11a - b) = 121a² - 11ab - 11ab + b² = 121a² - 22ab + b²

Next, let's simplify the product term: (9a + 7b)(8a - 13b) = 9a(8a - 13b) + 7b(8a - 13b) = 72a² - 117ab + 56ab - 91b² = 72a² - 61ab - 91b²

Now, let's combine the simplified terms: (11a - b)² + (9a + 7b)(8a - 13b) = 121a² - 22ab + b² + 72a² - 61ab - 91b² = 193a² - 83ab - 90b²

Therefore, the simplified expression is 193a² - 83ab - 90b².

2. (18x + 5y)(2x - 4y) - (6x - 3y)²

First, let's simplify the product term: (18x + 5y)(2x - 4y) = 18x(2x - 4y) + 5y(2x - 4y) = 36x² - 72xy + 10xy - 20y² = 36x² - 62xy - 20y²

Next, let's simplify the square term: (6x - 3y)² = (6x - 3y)(6x - 3y) = 36x² - 18xy - 18xy + 9y² = 36x² - 36xy + 9y²

Now, let's combine the simplified terms: (18x + 5y)(2x - 4y) - (6x - 3y)² = 36x² - 62xy - 20y² - (36x² - 36xy + 9y²) = 36x² - 62xy - 20y² - 36x² + 36xy - 9y² = 0x² - 26xy - 29y² = -26xy - 29y²

Therefore, the simplified expression is -26xy - 29y².

3. 4x(3x - 2y) - (10y - 0.4x)²

First, let's simplify the product term: 4x(3x - 2y) = 12x² - 8xy

Next, let's simplify the square term: (10y - 0.4x)² = (10y - 0.4x)(10y - 0.4x) = 100y² - 4xy - 4xy + 0.16x² = 100y² - 8xy + 0.16x²

Now, let's combine the simplified terms: 4x(3x - 2y) - (10y - 0.4x)² = 12x² - 8xy - (100y² - 8xy + 0.16x²) = 12x² - 8xy - 100y² + 8xy - 0.16x² = 11.84x² - 100y²

Therefore, the simplified expression is 11.84x² - 100y².

4. (15a + 2b)² - (3a - 7b)(3b - 5a)

First, let's simplify the square term: (15a + 2b)² = (15a + 2b)(15a + 2b) = 225a² + 30ab + 30ab + 4b² = 225a² + 60ab + 4b²

Next, let's simplify the product term: (3a - 7b)(3b - 5a) = 3a(3b - 5a) - 7b(3b - 5a) = 9ab - 15a² - 21b² + 35ab = 44ab - 15a² - 21b²

Now, let's combine the simplified terms: (15a + 2b)² - (3a - 7b)(3b - 5a) = 225a² + 60ab + 4b² - (44ab - 15a² - 21b²) = 225a² + 60ab + 4b² - 44ab + 15a² + 21b² = 240a² + 16ab + 25b²

Therefore, the simplified expression is 240a² + 16ab + 25b².