Answer:

1

How do you factorise (x+2)2–(2x+1)2 completely?

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Joseph DeAgostino

Answered January 15, 2020

How do you factorize (x+2) 2 –(2x+1) 2 completely?

Answer:

CONFUSED at first.

But: x2−y2=(x+y)(x−y)

(x+2)2−(2x+1)2 = ((x+2)+(2x+1))((x+2)−(2x+1))

=(3x+3)(−x+1)

= 3(x + 1)(1 - x)

Harikirtan Worlu

Michael Tam

Answered September 19

Method 1: Difference of squares

(x + 2)^2 - (2x + 1)^2 = ((x + 2) + (2x + 1))((x + 2) - (2x + 1))

= (3x + 3)(x + 2 - 2x - 1)

= 3 (x + 1)(-x + 1)

= -3 (x + 1)(x - 1)

Method 2: Simplify to collect LIKE terms, then factor

(x + 2)^2 - (2x + 1)^2 = x^2 + 4x + 4 - (4x^2 + 4x + 1)

= x^2 + 4x + 4 - 4x^2 - 4x - 1

= -3x^2 + 3

= -3 (x^2 - 1)

=- 3 (x + 1)(x - 1)

Method 3: Substitution

Let u = x + 2. Then 2u = 2x + 4. 2u - 3 = 2x + 1

(x + 2)^2 - (2x + 1)^2 = u^2 - (2u - 3)^2

=u^2 - (4U^2 - 12u + 9)

= u^2 - 4u^2 + 12u - 9

= -3u^2 + 12u - 9

= -3(u^2 - 4u + 3)

= -3 (u - 1)(u - 3)

= -3 ((x + 2 - 1)(x+ 2 - 3)

= -3 (x + 1)(x - 1)

Out of the 3 methods, method #1 is the most direct.