Question

simplify please dont write useless question i really want help​

Answer 1

Answer:

Mark me as a Brainliest pls

Step-by-step explanation:

ur answer is there in image

is it plus 25x² or -25x² please be clear

Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:\dfrac{ {25x}^{2} - 10x + 1}{5x - 1}$

can be rewritten as

$\rm \:  =  \:\dfrac{ {(5x)}^{2} - 2 \times 5x \times 1 + {(1)}^{2} }{5x - 1}$

We know,

$\boxed{ \tt{ \: {x}^{2} - 2xy + {y}^{2} = {(x - y)}^{2} \: }}$

So, using this, we get

$\rm \:  =  \:\dfrac{ {(5x - 1)}^{2} }{5x - 1}$

$\rm \:  =  \:\dfrac{ \cancel{(5x - 1)} \: (5x - 1)}{ \cancel{5x - 1}}$

$\rm \:  =  \:5x - 1$

Hence,

$\rm :\longmapsto\:\boxed{ \tt{ \: \dfrac{ {25x}^{2} - 10x + 1}{5x - 1} = 5x - 1 \: }}$

Alternative Method

Given expression is

$\rm :\longmapsto\:\dfrac{ {25x}^{2} - 10x + 1}{5x - 1}$

So, using long division we have

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\: \: \: \: \: \: \:5x - 1 \: \: \: \: \:\:}}}\\ {{\sf{5x - 1 }}}& {\sf{\: {25x}^{2} - 10x + 1 \:}} \\{\sf{}}&\underline{\sf{\: \: \: - {25x}^{2} + 5x \: \: \: \: \: \: \: \: \: \: \:}}\\{\sf{}}&{\sf{\: \: \: \: \: \: \: \: \: \: \: \: - 5x + 1 \:\:}}\\{\sf{}}&\underline{\sf{\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: 5x + 1 \:\:}}\\{\sf{}}&\underline{\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 0 \: \: }}\end{array}\end{gathered}\end{gathered}\end{gathered}$

Hence,

$\rm :\longmapsto\:\boxed{ \tt{ \: \dfrac{ {25x}^{2} - 10x + 1}{5x - 1} = 5x - 1 \: }}$

More to know :-

$\boxed{ \tt{ \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \: }}$

$\boxed{ \tt{ \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \: }}$

$\boxed{ \tt{ \: (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}$

$\boxed{ \tt{ \: {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2}) \: }}$

$\boxed{ \tt{ \: {(x + y)}^{2} - {(x - y)}^{2} = 4xy \: }}$