Question

Factorise:x^2+3xy-18y^2​

Answer 1

Step-by-step explanation:

Simplifying

x2 + 3xy + -18y2 = 0

Reorder the terms:

3xy + x2 + -18y2 = 0

Solving

3xy + x2 + -18y2 = 0

Solving for variable 'x'.

Factor a trinomial.

(x + -3y)(x + 6y) = 0

Subproblem 1

Set the factor '(x + -3y)' equal to zero and attempt to solve:

Simplifying

x + -3y = 0

Solving

x + -3y = 0

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

Add '3y' to each side of the equation.

x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0

x + 0 = 0 + 3y

x = 0 + 3y

Remove the zero:

x = 3y

Simplifying

x = 3y

Subproblem 2

Set the factor '(x + 6y)' equal to zero and attempt to solve:

Simplifying

x + 6y = 0

Solving

x + 6y = 0

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

Add '-6y' to each side of the equation.

x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0

x + 0 = 0 + -6y

x = 0 + -6y

Remove the zero:

x = -6y

Simplifying

x = -6y

Solution

x = {3y, -6y}