Factor 15x^2y^2−3x^3y+75x^4 . show your work.

Simplifying

3x4 + -75x2 = 0

Reorder the terms:

-75x2 + 3x4 = 0

Solving

-75x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x2'.

3x2(-25 + x2) = 0

Factor a difference between two squares.

3x2((5 + x)(-5 + x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x2' equal to zero and attempt to solve:

Simplifying

x2 = 0

Solving

x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x2 = 0

Take the square root of each side:

x = {0}

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying

5 + x = 0

Solving

5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.

5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0

0 + x = 0 + -5

x = 0 + -5

Combine like terms: 0 + -5 = -5

x = -5

Simplifying

x = -5

Subproblem 3

Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying

-5 + x = 0

Solving

-5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0

0 + x = 0 + 5

x = 0 + 5

Combine like terms: 0 + 5 = 5

x = 5  

Simplifying

x = 5

Solution

x = {0, -5, 5}

answer

step-by-step explanation: