Quickly answer -

how do i factor expressions with variables?

There are many different types of expressions.

To factor expressions with variables, the first thing is to take out any common factors always across all terms.

                          Ex: 5x + 15

                              = 5(x + 3)

To factor trinomials with one variable (standard form): , after taking out the common factor if there is one, you can:

i) Use the quadratic formula.

ii) Decomposition (factors of a and c multiply and added to give b)

Ex: 2x² - 7x + 3         2 * -3 = -6

(2                   -1 )         1 * -1 = -1

(1                   -3 )                      -6 + -1 = -7

=(2x-1)(x-3)

Trinomials with two variables like: ax² + bxy + cy² = 0

Use decomposition but include the second variable.

Ex: 2x² - 7xy + 3y²         2 * -3 = -6

(2                   -1 )         1 * -1 = -1

(1                   -3 )                      -6 + -1 = -7

=(2x-1y)(x-3y)

When a square value is being subtracted from another square value.

Difference of squares: = (√x² - √y²)(√x² + √y²)

Ex: 36x² - k²

= (6x - k)(6x + k)

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

sorry not sure

step-by-step explanation: