Math, asked by Raseshbava, 6 months ago

the value of (x+2y+2z)^2​

Answers

Answered by Alok001a
1

Answer:

x² + 4y² + 4z² × 4xy + 8yz + 4xz

Step-by-step explanation:

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please mark as brainliest

Answered by Flaunt
61

\huge\bold{\gray{\sf{Answer:}}}

\bold{Explanation:}

Identity is used :

 \sf{(a + b + c)}^{2}  =  {a}^{2}  +  {b}^{2}  +  {c}^{2}  + 2ab + 2bc + 2ca

=>Here ,a=x ,b=2y and c=2z

Now ,put into identity :

 \sf=  >  {(x + 2y + 2z)}^{2}  =  {x}^{2} +  {(2y)}^{2}   +  {(2z)}^{2}  + 2(x)(2y) + 2(2y)(2z) + 2(2z)(x)

 \sf=  >  {x}^{2}  +  {4y}^{2}  +  {4z}^{2}  + 4xy + 8yz + 4xz

 \sf=  >  {x}^{2}  + 4( {y}^{2}  +  {z}^{2} ) + 4(xy + 2yz + xz)

 \sf=  >  {\red{{(x + 2y + 2z)}^{2}  }}={\bold{{x}^{2}  + 4( {y}^{2}  +  {z}^{2} ) + 4(xy + 2yz + xz)}}

Other Identities =>

  • \bold{\boxed{ {(x -y)}^{2}  =  {x}^{2}  +  {y}^{2}  - 2xy}}
  • \bold{\boxed{ {x}^{3}   +   {y}^{3}  =  {x}^{3}  +  {y}^{3}   + 3xy(x + y)}}
  • \bold{\boxed{(x + y)(x  + z) =  {x}^{2}  + (y+ z)x + yz}}
  • \bold{\boxed{ {(x +y)}^{3}  =  {x}^{3}  +  {y}^{3}  +3xy[x+y]}}

  • \bold{\boxed{(x + a)(x - b) =  {x}^{2}  + (a - b)x - ab}}
  • \bold{\boxed{(x - a)(x - b) =  {x}^{2}  - (a + b)x + ab}}
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