Question

33.16. 1) (6-x) - x²(16-x)-2x² + 116; 2) (y+7ỷ +y(13 – y) = 21y® + 23; 3) (4-32) + 2(14+272²)-1082² +77; 4) (5x+2)³-25x(5x²-4)-150x² +21.​

Answer 1

Ответ:

1. -×^3 + 3x^2 - 10x + 110

2. y^2 + 6y - 1 = 0

3. -1082^2 + 2*272^2 + 301

4. 125×^3 + 50×^2 + 20x + 2

Answer 2

Let's simplify each of the given expressions:

1. (6-x) - x²(16-x) - 2x² + 116:

First, distribute x² into the second term:

= (6 - x) - (16x² - x³) - 2x² + 116

Now, combine like terms:

= 6 - x - 16x² + x³ - 2x² + 116

Rearrange the terms in descending order of the degree of x:

= x³ - 16x² - 2x² - x + 6 + 116

Combine the x² terms:

= x³ - 18x² - x + 6 + 116

Combine constants:

= x³ - 18x² - x + 122

So, the simplified expression is:

x³ - 18x² - x + 122

2. (y+7ỷ + y(13 – y) = 21y® + 23:

It seems like there are some unusual characters in this expression. Assuming you meant to write:

(y + 7y + y(13 - y)) = 21y² + 23

First, simplify the expression inside the parentheses:

= (y + 7y + 13y - y²) = 21y² + 23

Combine like terms:

= (21y + 13y - y²) = 21y² + 23

Combine like terms on the left side:

= (34y - y²) = 21y² + 23

Now, rearrange the equation to have all terms on one side:

34y - y² - 21y² - 23 = 0

Combine the y² terms:

= -y² - 21y² + 34y - 23 = 0

Combine like terms:

= -22y² + 34y - 23 = 0

So, the simplified equation is:

-22y² + 34y - 23 = 0

3. (4-32) + 2(14+272²) - 1082² + 77:

Let's simplify this expression step by step:

= (4 - 32) + 2(14 + 272²) - 108² + 77

= (-28) + 2(14 + 272²) - 108² + 77

Now, calculate the value inside the parentheses and exponents:

= (-28) + 2(14 + 73984) - 11664 + 77

= (-28) + 2(74098) - 11664 + 77

Now, multiply 2 by 74098:

= (-28) + 148196 - 11664 + 77

Now, combine the constants:

= 148196 - 11664 - 28 + 77

= 136481

So, the simplified expression is:

136481

4. (5x+2)³ - 25x(5x²-4) - 150x² + 21:

Let's simplify this expression step by step:

= (5x + 2)³ - 25x(5x² - 4) - 150x² + 21

First, calculate (5x + 2)³ using the binomial expansion formula or by multiplying it out:

= (125x³ + 150x² + 60x + 8) - 25x(5x² - 4) - 150x² + 21

Now, distribute -25x into the second term:

= 125x³ + 150x² + 60x + 8 - (125x³ - 100x) - 150x² + 21

Now, distribute -1 into the second term within the parentheses:

= 125x³ + 150x² + 60x + 8 - 125x³ + 100x - 150x² + 21

Now, combine like terms:

= 125x³ - 125x³ + 150x² - 150x² + 60x + 100x + 8 + 21

= 160x + 29

So, the simplified expression is:

160x + 29