Question

(р³ – 6p²+ 12р – 8) + 729p³ = (p -[] )³ + ( []p) ³=​

Answer 1

Ответ на фото надеюсь всё понятно?

Answer 2

To simplify the given expression, let's start by expanding the cubes on both sides of the equation:

(p - [] )³ + ([]p)³

Expanding the cubes using the binomial expansion formula:

(p - [] )³ = p³ - 3p²[] + 3p[]² - []³ ([]p)³ = []³p³ = 729p³

Now let's substitute these values back into the original equation:

(p³ – 6p² + 12p – 8) + 729p³ = p³ - 3p²[] + 3p[]² - []³ + 729p³

Combining like terms:

p³ + 729p³ - 6p² + 12p - 8 = p³ - 3p²[] + 3p[]² - []³ + 729p³

Rearranging the terms:

730p³ - 6p² + 12p - 8 = p³ - 3p²[] + 3p[]² - []³

To make the equation simpler, we can equate the corresponding coefficients:

730p³ = p³ -6p² = -3p²[] 12p = 3p[]² -8 = -[]³

From the first equation, we can see that 730p³ = p³. This implies that p = 0, as the only way for both sides of the equation to be equal is if p equals zero.

Substituting p = 0 into the second equation:

-6(0)² = -3(0)²[] 0 = 0

This equation is always true, so it doesn't provide any further information about the value of [].

Similarly, substituting p = 0 into the third equation:

12(0) = 3(0)[]² 0 = 0

Again, this equation is always true and doesn't provide any information about the value of [].

Finally, substituting p = 0 into the fourth equation:

-8 = -[]³

This equation implies that []³ = 8, and thus [] = 2, since 2³ = 8.

Therefore, the simplified expression is:

(p - 2)³ + (2p)³