Question

Раскройте скобки применив формулы квадрат суммы или квадрат разности 1) (a-10B)²= 2) (4m+1)²= 3) (2t-22)²= 4) (p+t) ²= 5) (m²-2c³) ²= Решите уравнение (2x-1) ²=4x²+37= Упростите выражение (5x+2)²-(5x+3)²= Докажите тождество (a+1)×(a-1)+(a+1) ²=2a×(a+1)

Answer 1

Ответ:

(a - 10)**2 = a**2 - 20a + 100

(4m + 1)**2 = 16m**2 + 8m + 1

(2t - 22)**2 = 4t**2 - 88t + 484

(p + t)**2 = p**2 + 2pt + t**2

(m**2 - 2c**3)**2 = m**4 - 4m**2c**3 + 4c**6

(2x - 1)**2 = 4x**2 + 37

4x**2 - 4x + 1 = 4x**2 + 37

- 4x = 37 - 1

- 4x = 36

x = 36/(-4)

x = - 9

(5x + 2)**2 - (5x + 3)**2 = (5x + 2 - (5x + 3))(5x + 2 + 5x + 3) = 5(10x + 5) = 50x + 250

(a + 1)(a - 1) + (a + 1)**2 = 2a(a + 1)

(a + 1)(a - 1 + a + 1) = 2a(a + 1)

(a + 1)2a = 2a(a + 1)

Объяснение:

a**c — число "а" в степени "с", например 2**5 — число "2" в степени "5".

Answer 2

1. (a-10B)² = a² - 20aB + 100B²
2. (4m+1)² = 16m² + 8m + 1
3. (2t-22)² = 4t² - 88t + 484
4. (p+t)² = p² + 2pt + t²
5. (m²-2c³)² = m⁴ - 4c³m² + 4c⁶

To solve the equation (2x-1)² = 4x² + 37, we can start by expanding the left side of the equation:

(2x-1)² = 4x² - 4x + 1

Now we can set this equal to the right side of the equation and solve for x:

4x² - 4x + 1 = 4x² + 37

Subtracting 4x² from both sides gives:

-4x + 1 = 37

Subtracting 1 from both sides gives:

-4x = 36

Dividing both sides by -4 gives:

x = -9

So the solution to the equation is x = -9.

To simplify the expression (5x+2)² - (5x+3)², we can expand both squares and then combine like terms:

(5x+2)² - (5x+3)² = (25x² + 20x + 4) - (25x² + 30x + 9)

Removing the parentheses and combining like terms gives:

25x² + 20x + 4 - 25x² - 30x - 9

Combining like terms further gives:

-10x - 5

So the simplified expression is -10x - 5.

To prove the identity (a+1) × (a-1) + (a+1)² = 2a × (a+1), we can start by expanding both sides:

Left side: (a+1) × (a-1) + (a+1)² = a² - a + a - 1 + a² + 2a + 1 = 2a² + 2a

Right side: 2a × (a+1) = 2a² + 2a

Since the left side and the right side are equal, we have proved the identity (a+1) × (a-1) + (a+1)² = 2a × (a+1).