Math, asked by priyal, 1 month ago

simplify please dont write useless question i really want help​

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Answered by pranay9018
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

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Answered by mathdude500
6

\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 \: }}

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