Question

А) х(х + 2) – (х + 3)(х – 3) = 15; б) 4у(у – 1) – (2у – 5)(2у + 5) = 1;в) 3х – 5(х + 1)(х – 1) + 5(х + 2)(х – 2) = 6;г) (х + 1)2 – (х – 3)2 = 8. упростить выражения ​

Answer 1

Ответ:

Фото

Объяснение:

Answer 2

А) Let's simplify the expression:

x(x + 2) - (x + 3)(x - 3) = 15

Expanding the brackets:

x^2 + 2x - (x^2 - 9) = 15

Simplifying further:

x^2 + 2x - x^2 + 9 = 15

The x^2 terms cancel out:

2x + 9 = 15

Subtracting 9 from both sides:

2x = 6

Dividing both sides by 2:

x = 3

So the solution to the equation is x = 3.

Б) Let's simplify the expression:

4y(y - 1) - (2y - 5)(2y + 5) = 1

Expanding the brackets:

4y^2 - 4y - (4y^2 - 25) = 1

Simplifying further:

4y^2 - 4y - 4y^2 + 25 = 1

The 4y^2 terms cancel out:

-4y - 4y^2 + 25 = 1

Subtracting 25 from both sides:

-4y - 4y^2 = -24

Dividing both sides by -4:

y + y^2 = 6

Rearranging the equation:

y^2 + y - 6 = 0

Factoring the quadratic equation:

(y + 3)(y - 2) = 0

Setting each factor to zero:

y + 3 = 0 -> y = -3 y - 2 = 0 -> y = 2

So the solutions to the equation are y = -3 and y = 2.

В) Let's simplify the expression:

3x - 5(x + 1)(x - 1) + 5(x + 2)(x - 2) = 6

Expanding the brackets:

3x - 5(x^2 - 1) + 5(x^2 - 4) = 6

Simplifying further:

3x - 5x^2 + 5 + 5x^2 - 20 = 6

The x^2 terms cancel out:

3x - 15 = 6

Adding 15 to both sides:

3x = 21

Dividing both sides by 3:

x = 7

So the solution to the equation is x = 7.

Г) Let's simplify the expression:

(x + 1)^2 - (x - 3)^2 = 8

Expanding the squares:

x^2 + 2x + 1 - (x^2 - 6x + 9) = 8

Simplifying further:

x^2 + 2x + 1 - x^2 + 6x - 9 = 8

The x^2 terms cancel out and the x terms combine:

8x - 8 = 8

Adding 8 to both sides:

8x = 16

Dividing both sides by 8:

x = 2

So the solution to the equation is x = 2.

I have simplified the expressions and provided the solutions to each equation.