Question

1) 9х²-49у² 2) 0,36а^4-b² 3) (x-5)²-2х(х-3) 4) (3а-1)²+6(а+2)

Answer 1

Здесь формулы сокращённо го умножения

1) (3х-7у)(3х+7у)

2) (0,6а^2-в)(0,6а^2+в)

3) =х^2-10х+25-2х^2+6х= х^2-4х+25.

4) =9а^2-6а+1+6а+12= 9а^2+13

Answer 2

To simplify the given expressions, let's work on each one step by step:

1. 9x² - 49y²: This is a difference of squares, which can be simplified using the identity (a² - b²) = (a + b)(a - b).

9x² - 49y² = (3x)² - (7y)² = (3x + 7y)(3x - 7y).

2. 0.36a^4 - b²: This expression cannot be further simplified unless we know more about the variables. However, we can rewrite 0.36 as (0.6)².

0.36a^4 - b² = (0.6a²)² - b² = (0.6a² + b)(0.6a² - b).

3. (x - 5)² - 2x(x - 3): Let's expand the squared term and then simplify:

(x - 5)² - 2x(x - 3) = (x - 5)(x - 5) - 2x(x - 3).

Expanding further:

= (x² - 5x - 5x + 25) - (2x² - 6x).

Now, combine like terms:

= (x² - 10x + 25) - 2x² + 6x.

= x² - 2x² - 10x + 6x + 25.

= -x² - 4x + 25.

4. (3a - 1)² + 6(a + 2): Let's expand the squared term and then simplify:

(3a - 1)² + 6(a + 2) = (3a - 1)(3a - 1) + 6(a + 2).

Expanding further:

= (9a² - 3a - 3a + 1) + (6a + 12).

Now, combine like terms:

= (9a² - 6a + 1) + 6a + 12.

= 9a² + 1 + 6a + 12.

= 9a² + 6a + 13.

So, the simplified expressions are:

1. 9x² - 49y² = (3x + 7y)(3x - 7y).
2. 0.36a^4 - b² = (0.6a² + b)(0.6a² - b).
3. (x - 5)² - 2x(x - 3) = -x² - 4x + 25.
4. (3a - 1)² + 6(a + 2) = 9a² + 6a + 13.