Question

Y=(x+5)|x-3|-(x-5)|x+3|;​

Answer 1

Ответ:

у(-х)=(-х+5)*|-x-3|-(-x-5)*|-x+3|=-(x-5)|x+3|+(x+5)*|x-3|=y(x)

Пошаговое объяснение:

Answer 2

Ответ:

не это? просто похоже...

Answer 3

To simplify the expression Y = (x + 5)|x - 3| - (x - 5)|x + 3|, you can break it down into cases based on the sign of the expressions inside the absolute values (|x - 3| and |x + 3|). Let's consider these cases:

Case 1: x < -3 In this case, both |x - 3| and |x + 3| are negative, so they become -1: Y = (x + 5)(-1) - (x - 5)(-1)

Now, distribute the negative sign and simplify: Y = -x - 5 + x - 5

The x terms cancel out: Y = -10

Case 2: -3 ≤ x < 3 In this case, |x - 3| is negative, and |x + 3| is positive, so we have: Y = (x + 5)(-1) - (x - 5)(x + 3)

Now, distribute the negative sign and simplify: Y = -x - 5 - (x^2 - 2x - 15)

Combine like terms: Y = -x - 5 - x^2 + 2x + 15

Y = -x - x^2 + 2x + 10

Simplify further: Y = -x^2 + x + 10

Case 3: x ≥ 3 In this case, both |x - 3| and |x + 3| are positive, so they remain unchanged: Y = (x + 5)(x - 3) - (x - 5)(x + 3)

Now, expand and simplify: Y = x^2 + 5x - 3x - 15 - x^2 + 5x + 3x - 15

Combine like terms: Y = 2x^2 - 30

So, depending on the value of x, the expression Y simplifies to different forms:

1. If x < -3, then Y = -10.
2. If -3 ≤ x < 3, then Y = -x^2 + x + 10.
3. If x ≥ 3, then Y = 2x^2 - 30.