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

Let's factorize in

ℝ

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

For

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

, we recognize a difference of two squares:

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

. Apply

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

, with

a = 2 x

and

b = 2 x + 3

You can write the expression:

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

in factored form:

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

Let's factor in

ℝ

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

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (2 x + 3)

- 2 x - 3

■Like terms are grouped by adding their coefficients:

2 x + 2 x

4 x

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

ⓘ Like terms are grouped by adding their coefficients:

2 x - 2 x

0

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

ⓘ Adding 0 changes nothing:

0 - 3

-3

▶Factored expression:

- 3 \cdot (4 x + 3)