Simplify (x+3y-6z)^2

${(x + 3 y - 6 z)}^{2}$

Step 1

Rewrite ${(x + 3 y - 6 z)}^{2}$ as $(x + 3 y - 6 z) (x + 3 y - 6 z)$ .

$(x + 3 y - 6 z) (x + 3 y - 6 z)$

Step 2

Expand $(x + 3 y - 6 z) (x + 3 y - 6 z)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x + x (3 y) + x (- 6 z) + 3 y x + 3 y (3 y) + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Step 3

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (3 y) + x (- 6 z) + 3 y x + 3 y (3 y) + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Rewrite using the commutative property of multiplication.

$x^{2} + 3 x y + x (- 6 z) + 3 y x + 3 y (3 y) + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Rewrite using the commutative property of multiplication.

$x^{2} + 3 x y - 6 x z + 3 y x + 3 y (3 y) + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Rewrite using the commutative property of multiplication.

$x^{2} + 3 x y - 6 x z + 3 y x + 3 \cdot 3 y \cdot y + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 3 \cdot 3 (y \cdot y) + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Multiply $y$ by $y$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 3 \cdot 3 y^{2} + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Multiply $3$ by $3$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} + 3 y (- 6 z) - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Rewrite using the commutative property of multiplication.

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} + 3 \cdot - 6 y z - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Multiply $3$ by $- 6$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 6 z (3 y) - 6 z (- 6 z)$

Rewrite using the commutative property of multiplication.

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 6 \cdot 3 z y - 6 z (- 6 z)$

Multiply $- 6$ by $3$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 18 z y - 6 z (- 6 z)$

Rewrite using the commutative property of multiplication.

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 18 z y - 6 \cdot - 6 z \cdot z$

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 18 z y - 6 \cdot - 6 (z \cdot z)$

Multiply $z$ by $z$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 18 z y - 6 \cdot - 6 z^{2}$

Multiply $- 6$ by $- 6$ .

$x^{2} + 3 x y - 6 x z + 3 y x + 9 y^{2} - 18 y z - 6 z x - 18 z y + 36 z^{2}$

Step 4

Add $3 x y$ and $3 y x$ .

Move $y$ .

$x^{2} + 3 x y + 3 x y - 6 x z + 9 y^{2} - 18 y z - 6 z x - 18 z y + 36 z^{2}$

Add $3 x y$ and $3 x y$ .

$x^{2} + 6 x y - 6 x z + 9 y^{2} - 18 y z - 6 z x - 18 z y + 36 z^{2}$

Step 5

Subtract $6 z x$ from $- 6 x z$ .

Move $z$ .

$x^{2} + 6 x y + 9 y^{2} - 18 y z - 6 x z - 6 x z - 18 z y + 36 z^{2}$

Subtract $6 x z$ from $- 6 x z$ .

$x^{2} + 6 x y + 9 y^{2} - 18 y z - 12 x z - 18 z y + 36 z^{2}$

Step 6

Subtract $18 z y$ from $- 18 y z$ .

Move $z$ .

$x^{2} + 6 x y + 9 y^{2} - 18 y z - 18 y z - 12 x z + 36 z^{2}$

Subtract $18 y z$ from $- 18 y z$ .

$x^{2} + 6 x y + 9 y^{2} - 36 y z - 12 x z + 36 z^{2}$

Step 7

Move $- 36 y z$ .

$x^{2} + 6 x y + 9 y^{2} - 12 x z - 36 y z + 36 z^{2}$

Step 8

Move $9 y^{2}$ .

$x^{2} + 6 x y - 12 x z + 9 y^{2} - 36 y z + 36 z^{2}$

Simplify (x+3y-6z)^2

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