Question

evaluate (3x+2y+z)^2​

Answer 1

$\huge\mathfrak\green{\bold{\underline{☘{ ℘ɧεŋσɱεŋศɭ}☘}}}$

$\huge\tt\red{\bold{\underline{\underline{❥Question᎓}}}}$evaluate (3x+2y+z)^2

$\huge\tt{\boxed{\overbrace{\underbrace{\blue{Answer</p><p> }}}}}$

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Here this identity is used:-

$\red {(a + b + c)}^{2} = \green{a}^{2} \bold{+} \green{b}^{2} \bold{ + } \green{c}^{2} + \green{2ab }\bold{+ }\green{2bc }+ \green{2ca}$

Now here a=3x,b=2y and c=z

${(3x + 2y + z)}^{2} = {(3x)}^{2} + {(2y)}^{2} + {z}^{2} + 2(3x)(2y) + 2(2y)(z) + 2(z)( 3x)$

${(3x + 2y + z)}^{2} = 9 {x}^{2} + 4 {y}^{2} + {z}^{2} + 12xy + 8yz + 6xz$

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Answer 2

AnsweR :-

$\sf {(3x + 2y + z)}^{2}$

$\sf {3x}^{2} + {2y}^{2} + {z}^{2} + 2(3x \times 2y) + 2(2y \times z) + 2(z \times 3x)$

$\sf {9x}^{2} + {4y}^{2} + {z}^{2} + 12xy + 4yz + 6zx$

Procedure :-

$\implies$ This expression is from Algebraic identites. In this we have to evaluate the whole equation.

$\implies$ We can see that it has 2 as whole square so we will use 5th indentity of Algerbric identites, which is

(a+b+c)² = a²+ b²+ c²+ 2ab + 2bc + 2ca.

$\implies$ Then we will square the numbers and then first multiply it with in the brackets as shown in the answer above and then multiply it with 2 which is outside the bracket And hence the answer of your question is

9x²+ 4y²+ z²+ 12xy+ 4yz+ 6zx.

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