factor 16x^3-100x — step-by-step solution

Let's factorize in

ℝ

16 x^{3} - 100 x

You can factorize this expression into:

x \cdot (16 x^{2} - 100)

⇥Let's factor in

ℝ

(16 x^{2} - 100)

⇥We factor out

4

, the greatest common divisor of the coefficients:

16 x^{2} - 100

4 \cdot (4 x^{2} - 25)

⇥For

4 x^{2} - 25

, we recognize a difference of two squares:

{(2 x)}^{2} - 5^{2}

. Apply

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

, with

a = 2 x

and

b = 5

⇥You can write the expression:

4 x^{2} - 25

in factored form:

(2 x - 5) \cdot (2 x + 5)

▷The factor

(16 x^{2} - 100)

factors as:

4 \cdot (2 x + 5) \cdot (2 x - 5)

ⓘ Factor out the common factor

x

▶Factored expression:

4 x \cdot (2 x + 5) \cdot (2 x - 5)