Question

Expand the following (2x+y+3z)^2

Answer 1

Hope it helps ................

Answer 2

(2x + y + 3z)² = 4x² + y² + 9z² + 4xy + 6yz + 12xz

Given :

The expression (2x + y + 3z)²

To find :

Expand the expression

Formula :

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

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is (2x + y + 3z)²

Step 2 of 2 :

Expand the expression

We are aware of the formula that

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

Thus we get

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

$\displaystyle \sf{ = {(2x)}^{2} + {( y)}^{2} + {( 3z)}^{2} + 2.2x.y + 2.y.3z + 2.2x.3z }$

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

∴ (2x + y + 3z)² = 4x² + y² + 9z² + 4xy + 6yz + 12xz

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