Question

factorize
$gx {}^{2} - 30x + 25$

Answer 1

ᴇʟʟᴏ!!

ʜᴇʀᴇ's ʏᴏᴜʀ ᴀɴsᴡᴇʀ

____________________

• ғᴀᴄᴛᴏʀɪᴇs ᴏғ ᴛʜᴇ ғᴏʟʟᴏᴡɪɴɢ :-

9x^2 - 30x + 25

= ( 3x )^2 - 2 . 3x . 5 + ( 5 )^2 

= ( 3x - 5 )^2 [ • ( ᴀ - ʙ )^2 = ᴀ^2 - 2ᴀʙ + ʙ^2 ]

= ( 3x - 5 ) ( 3x - 5 )

___________________

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ ᴅᴇᴀʀ!

★ ᴅᴇᴠɪʟ ᴋɪɴɢ

Answer 2

$\textbf{\underline{Solution -}}$

♢ 9x² - 30x + 25

= (3x)² - 2(3x) (5) + (5)²

= (3x - 5)²

= $\boxed{(3x - 5) (3x - 5)}$

$\textbf{Identity used -}$

a² - 2ab + b² = (a - b)²

$\textbf{\underline{Explaination -}}$

Here, we had factorised the following with identity (a - b)²

where,

a² = (3x)²

b² = (5)²

In the question, we had first broke the numbers into their smallest factors...

i.e.

9x² = (3x)²

25 = (5)²

And by using identity...

a² - 2ab + b² = (3x)² - 2(3x) (5) + (5)²

= (a - b)² = (3x - 5)²

We know,

(3x - 5)² = (3x - 5) (3x - 5)

$\textbf{Note -}$ It is not the only way to factorise it, we can also use middle term factor, where the middle term is splitted...

#$\textbf{Be Brainly}$