Question

(x + 2y + 3z)²=


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Answer 1

Topic

Algebraic Identities

To Solve

( x + 2y + 3z )²

Solution

Technique 1

Use multiplication method

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

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

x² + 2xy + 3zx + 2xy + 4y² + 6yz + 3zx + 6zy + 9z²

x² + 4y² + 9z² + 3zx + 3zx + 2xy + 2xy + 6yz + 6yz

x² + 4y² + 9z² + 6xz + 4xy + 12yz

Technique 2

Use formula,

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

here

• a = x

• b = 2y

• c = 3z

Apply the formula,

( x + 2y + 3z )²

x² + (2y)² + (3z)² + 2(x)(2y) + 2(2y)(3z) + 2(3z)(x)

x² + 4y² + 9z² + 4xy + 12yz + 6xz

Answer

So, answer is,

x² + 4y² + 9z² + 4xy + 12yz + 6xz

which is option A.