Question

Factorise each of the following.
(a) (2x + 1)² - 10(2x + 1) + 25​

Answer 1

Answer:

(2x+1)(2x+1-10+25)

(2x+1)(2x+16)

Answer 2

Answer :-

4(x - 2)(x - 2).

Explanation :-

Here, we have to factorise an expression.

So, Let's Begin.

⇒ (2x + 1)² - 10(2x + 1) + 25.

Use Identity : (a + b)² = a² + b² + 2ab.

⇒ (2x)² + (1)² + 2(2x)(1) - 20x - 10 + 25.

⇒ 4x² + 1 + 4x - 20x - 10 + 25.

⇒ 4x² - 16x + 1 - 10 + 25.

⇒ 4x² - 16x + 16.

Taking 4 as common,

⇒ 4{x² - 4x + 4}.

Use Splitting Middle term method.

⇒ 4{x² - 2x - 2x - 4}.

⇒ 4{x(x - 2) - 2(x - 2)}.

⇒ 4(x - 2)(x - 2).

Therefore, Answer = 4(x - 2)(x - 2).