factor (3x+1)^2-(x-4)^2 — step-by-step solution

Let's factor in

ℝ

{(3 x + 1)}^{2} - {(x - 4)}^{2}

We recognize a difference of two squares:

{(3 x + 1)}^{2} - {(x - 4)}^{2}

. Apply

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

, with

a = 3 x + 1

and

b = x - 4

You can factorize this expression into:

((3 x + 1) - (x - 4)) \cdot ((3 x + 1) + (x - 4))

ℹ

- (x - 4)

- x + 4

‖

1 - 4

-3

‖

3 x + x

4 x

(3 x

+ 1

- x

+ 4) \cdot (4 x - 3)

ℹ

1 + 4

5

‖

3 x - x

2 x

▶Factored expression:

(2 x + 5) \cdot (4 x - 3)