How do i factor this x^3y-4xy, and x^4+27x?

Question

How do i factor this x^3y-4xy, and x^4+27x?

Answer 1

1. x^3y - 4xy =

Look at each term's factors.

x^3y = x*x*x*y

-4xy = -1*4*x*y

Both of them have x*y in common so factor that out.

xy(x^2 - 4) =

Notice that x^2 - 4 is the difference of two squares.

x^2 - 4 = (x)^2 - (2)^2

We know that:

a^2 - b^2 = (a - b)(a + b)

Given: x^2 - 4 = (x)^2 - (2)^2

Means: a = x, b = 2

Plug these into the formula.

x^2 - 4 = (x)^2 - (2)^2 = (x - 2)(x + 2)

Replace x^2 - 4 with the factored form in the whole equation.

xy(x^2 - 4) =

xy(x - 2)(x + 2)

ANSWER: x^3y - 4xy = xy(x - 2)(x + 2)

--------------------------------------...

2. x^4 + 27x =

Look at each term's factors.

x^4 = x*x*x*x

27x = 27*x

Both of them have x in common so factor that out.

x(x^3 + 27) =

Notice that x^3 + 27 is the sum of two cubes.

x^3 + 27 = (x)^3 + (3)^3

We know that:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Given: x^3 + 27 = (x)^3 + (3)^3

Means: a = x, b = 3

Plug these into the formula.

x^3 + 27 = (x)^3 + (3)^3 = (x + 3)(x^2 - 3x + 9)

Replace x^3 + 27 with the factored form in the whole equation.

x(x^3 + 27) =

x(x + 3)(x^2 - 3x + 9)

ANSWER: x^4 + 27x = x(x + 3)(x^2 - 3x + 9)

Answer 2

Simplifying

x3y + -4xy

Reorder the terms:

-4xy + x3y

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

xy(-4 + x2)

Factor a difference between two squares.

xy((2 + x)(-2 + x))

Final result:

xy(2 + x)(-2 + x)

Simplifying

x4 + 27x

Reorder the terms:

27x + x4

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

x(27 + x3)

Final result:

x(27 + x3)

Answer 3

1)

take (x^3y-4xy)

there is an xy in both x^3y and 4xy so we can take an xy out of them:

x^3y / xy = x^2

4xy / xy = 4

so we have:

(xy)(x^2-4) <=============

2)

we have: x^4+27x

there is an x in both x^4 and 27x

x^4 / x = x^3

27x / x = 27

so we end up with:

(x)(x^3 + 27) <===========