Factorize completely 4x^3 - 8x^2y - 9xy^2 + 18y^3

Simplifying

4x2 + 8xy + 4y2

Reorder the terms:

8xy + 4x2 + 4y2

Factor out the Greatest Common Factor (GCF), '4'.

4(2xy + x2 + y2)

Factor a trinomial.

4((x + y)(x + y))

Final result:

4(x + y)(x + y)

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is