Name: Factoring a difference of squares: solution walkthrough
Uploaded: 2026-11-13
Duration: 2 min 8 s
Description: Which of the following is the complete factorization of 16x² - 49? Try it, then watch the animated solution.

First look for a common factor:

16

and

49

share none. Then see two squares:

16x^2 = (4x)^2

and

49 = 7^2

.

Picture a square of side

4x

with a small square of side

7

cut from its corner. What is left has area

16x^2 - 49

.

Cut off the top strip and turn it on its side. The L becomes one rectangle,

4x + 7

long and

4x - 7

tall.

So

16x^2 - 49 = (4x - 7)(4x + 7)

. Check:

16x^2 + 28x - 28x - 49

; the middle terms cancel.

Traps:

(4x - 7)^2

has a middle term,

(4x - 49)(4x + 49)

skips the root of

49

,

(8x - 7)(8x + 7)

halves

16

.

Try it first