Question

factorize (x+2y+3z)x(x+2y+3z)​

Answer 1

Answer:

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

(x+2y + 3z)2 = x2 + 4y2 + 9z2 +4yx + 12zy + 6zx

Answer 2

$\huge\tt{\bold{\underline{\underline{Question᎓}}}}$

factorize (x+2y+3z)x(x+2y+3z)

$\huge\tt{\bold{\underline{\underline{Answer᎓}}}}$

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Here , this identity is used:

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

Here ,a=x;b=2y and c=3z

Now ,putting values into formula :

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

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

$= {x}^{2} + 4y(y + x) + 9 {z}^{2} + 12yz + 6zx$

$\bold{ = {x}^{2} + 4y(x + y) + 3z(3z + 4y + 2x)}$

Other Related formulas:

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

• $\bold{\boxed{{(a -b)}^{2} = {a}^{2} +{b}^{2} - 2ab }}$
• $\bold{\boxed{{(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a+b)}}$
• $\bold{\boxed{{(a -b)}^{3} = {a}^{3} + {b}^{3} - 3ab(a-b)}}$

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