Question

№1 (a+2b)(a²-2ab+4b²) №2 a)4a²-9b² б)-4x²+8x-4 №3 (2x-1)²=(2x+3)(2x-3) №4 4x²+y² > 4xy-5 №5 24²-11²/49²-36²

Answer 1

С 1 по 3 пошаговое объяснение

Answer 2

Sure, I'll help you with the expressions you provided:

№1: (a + 2b)(a² - 2ab + 4b²)

To simplify this expression, you can use the distributive property of multiplication:

(a + 2b)(a² - 2ab + 4b²) = a(a² - 2ab + 4b²) + 2b(a² - 2ab + 4b²)

Now, multiply each term:

a(a² - 2ab + 4b²) = a³ - 2a²b + 4ab² 2b(a² - 2ab + 4b²) = 2b³ - 4b²a + 8b³

The simplified expression is:

a³ - 2a²b + 4ab² + 2b³ - 4b²a + 8b³

№2: a) 4a² - 9b²

This expression seems to be already simplified. It's a binomial that cannot be factored further.

b) -4x² + 8x - 4

This expression also seems to be already simplified. It's a trinomial that cannot be factored further.

№3: (2x - 1)² = (2x + 3)(2x - 3)

Let's expand the left-hand side first:

(2x - 1)² = (2x - 1)(2x - 1)

To expand this, you can use the FOIL method:

(2x - 1)(2x - 1) = 4x² - 2x - 2x + 1 = 4x² - 4x + 1

Now let's simplify the right-hand side:

(2x + 3)(2x - 3) = 4x² - 6x + 6x - 9 = 4x² - 9

The statement (2x - 1)² = (2x + 3)(2x - 3) is not correct; they are not equal.

№4: 4x² + y² > 4xy - 5

To solve this inequality, let's move all terms to the left side:

4x² + y² - 4xy + 5 > 0

This is a quadratic inequality. To solve it, we need to find the critical points where the expression equals zero and determine the regions where it's greater than zero.

To find the critical points, we set the expression inside the inequality to zero:

4x² + y² - 4xy + 5 = 0

This quadratic equation may or may not have real solutions. It depends on the specific values of x and y. The inequality can't be simplified further without more information about the variables x and y.

№5: (24² - 11²) / (49² - 36²)

Let's calculate the expression:

(24² - 11²) / (49² - 36²) = (576 - 121) / (2401 - 1296) = 455 / 1105

The fraction 455/1105 cannot be simplified further since the numerator and denominator do not have any common factors other than 1.