Question

the value of (x+2y+2z)^2​

Answer 1

Answer:

x² + 4y² + 4z² × 4xy + 8yz + 4xz

Step-by-step explanation:

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Answer 2

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

$\bold{Explanation:}$

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 =>

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

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