Question

ТЕМА 3. МНОГОЧЛЕНЫ Упростить: 1) ( 3y-5) (y-2) -4*(2y-1)+9(y-2) 2) -4(a-3) -(a-2)+(2a-1)*(a+4) 3) 2*(x-4) - (x-2) (x+7)-3*(2-x) ОЧЕНЬ СРОЧНО!!!!!!! С ОБЪЯСНЕНИЕМ ПОЖАЛУЙСТА!1!!1!!

Answer 1

Упростить многочлены.

1. (3y - 5) * (y - 2) - 4 * (2y - 1) + 9 * (y - 2) =

  = 3y² - 6y - 5y + 10 - 8y + 4 + 9y - 18 =

  = 3y² - 10y - 4.

2. - 4 * (a - 3) - (a - 2) + (2a - 1) * (a + 4) =

  = - 4a + 12 - a + 2 + 2a² + 8a - a - 4 =

  = 2a² + 2a + 10.

3. 2 * (x - 4) - (x - 2) * (x + 7) - 3 * (2 - x) =

  = 2x - 8 - (x² + 7x - 2x - 14) - 6 + 3x =

  = 2x - 8 - x² - 5x + 14 - 6 + 3x =

  = - x².

P.S. Как всегда, сначала раскрываем скобки. Если перед скобкой "+", то знаки в скобках оставляем без изменения. А если перед скобкой "-", то все знаки в скобках меняются на противоположные. Дальше просто приводим подобные слагаемые. В ответе получаем упрощённый многочлен.

Answer 2

1. (3y - 5)(y - 2) - 4(2y - 1) + 9(y - 2)

Let's simplify each term step by step:

First, we'll apply the distributive property to the first term: (3y - 5)(y - 2) = 3y * y + 3y * (-2) - 5 * y - 5 * (-2) = 3y^2 - 6y - 5y + 10 = 3y^2 - 11y + 10

Next, we'll simplify the second term: -4(2y - 1) = -4 * 2y + (-4) * (-1) = -8y + 4

Lastly, we'll simplify the third term: 9(y - 2) = 9 * y + 9 * (-2) = 9y - 18

Now, we'll combine all the simplified terms: (3y - 5)(y - 2) - 4(2y - 1) + 9(y - 2) = 3y^2 - 11y + 10 - 8y + 4 + 9y - 18 = 3y^2 - 11y - 8y + 9y + 10 + 4 - 18 = 3y^2 - 10y - 4

Therefore, the simplified expression is 3y^2 - 10y - 4.

2. -4(a - 3) - (a - 2) + (2a - 1)(a + 4)

Again, let's simplify each term step by step:

-4(a - 3) = -4 * a + (-4) * (-3) = -4a + 12

-(a - 2) = -a + 2

(2a - 1)(a + 4) = 2a * a + 2a * 4 - 1 * a - 1 * 4 = 2a^2 + 8a - a - 4 = 2a^2 + 7a - 4

Now, let's combine all the simplified terms: -4(a - 3) - (a - 2) + (2a - 1)(a + 4) = -4a + 12 - a + 2 + 2a^2 + 7a - 4

Combine like terms: = 2a^2 - 4a - a + 7a - 4 + 12 + 2 = 2a^2 + 2a + 10

Therefore, the simplified expression is 2a^2 + 2a + 10.

3. 2(x - 4) - (x - 2)(x + 7) - 3(2 - x)

Let's simplify each term step by step:

2(x - 4) = 2x - 8

(x - 2)(x + 7) = x * x + x * 7 - 2 * x - 2 * 7 = x^2 + 7x - 2x - 14 = x^2 + 5x - 14

3(2 - x) = 3 * 2 - 3 * x = 6 - 3x

Now, let's combine all the simplified terms: 2(x - 4) - (x - 2)(x +