factor 2v^3-2v^3x^4 — step-by-step solution

1) Let's factorize in

ℝ

2 v^{3} - 2 v^{3} x^{4}

You can write the expression in factored form:

v^{3} \cdot (2 - 2 x^{4})

⇥1.1) Let's factor in

ℝ

(2 - 2 x^{4})

⇥We factor out

2

, the greatest common divisor of the coefficients:

2 - 2 x^{4}

2 \cdot (1 - x^{4})

⇥For

1 - x^{4}

, we recognize a difference of two squares:

1^{2} - {(x^{2})}^{2}

. Apply

a^{2} - b^{2} = (a - b) \cdot (a + b)

, with

a = 1

and

b = x^{2}

⇥You can factorize the expression:

1 - x^{4}

into:

(1 - x^{2}) \cdot (1 + x^{2})

⇥1.2) Let's factorize in

ℝ

(1 - x^{2}) \cdot (1 + x^{2})

⇥Let's factor in

ℝ

(1 - x^{2})

⇥For

1 - x^{2}

, we recognize a difference of two squares:

1^{2} - x^{2}

. Apply

a^{2} - b^{2} = (a - b) \cdot (a + b)

, with

a = 1

and

b = x

⇥Factors found:

(1 - x) \cdot (x + 1)

▷The factor

(2 - 2 x^{4})

factors as:

2 \cdot (1 - x) \cdot (x + 1) \cdot (x^{2} + 1)

ⓘ Factor out the common factor

v^{3}

▶Factored expression:

2 v^{3} \cdot (1 - x) \cdot (x + 1) \cdot (x^{2} + 1)