Question

(2х-6)²(х-6)=(2х-6)(х-6)²​

Answer 1

(2х- 6)²(х- 6)=(2х- 6)(х- 6)²​

(2х- 6)²(х- 6) - (2х- 6)(х- 6)²​ =0

(2х- 6)*(х- 6) *( (2х- 6) -(х- 6) ) = 0

(2х- 6)*(х- 6) *(  2х- 6 -х+6 ) = 0

(2х- 6)*(х- 6) * х= 0

(2х- 6)= 0 или (х- 6) =0  или  х= 0

х₁=3                   х₂=6               х₃=0

Answer 2

Let's expand both sides of the equation to see if they are equal:

Left-hand side (LHS): (2x - 6)² * (x - 6)

Using the formula for squaring a binomial (a + b)² = a² + 2ab + b², we can expand the first part: (2x - 6)² = (2x)² + 2 * (2x) * (-6) + (-6)² = 4x² - 24x + 36

Now we have: LHS = (4x² - 24x + 36) * (x - 6)

To expand further, we distribute each term of (4x² - 24x + 36) to (x - 6):

LHS = 4x² * x + 4x² * (-6) - 24x * x - 24x * (-6) + 36 * x + 36 * (-6) LHS = 4x³ - 24x² - 24x² + 144x + 36x - 216

LHS = 4x³ - 48x² + 180x - 216

Now, let's calculate the right-hand side (RHS): (2x - 6) * (x - 6)²

Using the formula for squaring a binomial (a - b)² = a² - 2ab + b², we can expand the second part: (x - 6)² = x² - 2 * x * 6 + 6² = x² - 12x + 36

Now we have: RHS = (2x - 6) * (x² - 12x + 36)

To expand further, we distribute each term of (2x - 6) to (x² - 12x + 36):

RHS = 2x * x² + 2x * (-12x) + 2x * 36 - 6 * x² - 6 * (-12x) - 6 * 36 RHS = 2x³ - 24x² + 72x - 6x² + 72x - 216

RHS = 2x³ - 30x² + 144x - 216

Now we can compare both sides of the equation:

LHS = 4x³ - 48x² + 180x - 216 RHS = 2x³ - 30x² + 144x - 216

As we can see, the left-hand side (LHS) is not equal to the right-hand side (RHS) of the equation, so the statement is false. The original equation (2x - 6)² * (x - 6) = (2x - 6) * (x - 6)² does not hold true.