Expand the Trigonometric Expression (2x-7y+7z)^2

${(2 x - 7 y + 7 z)}^{2}$

Step 1

Rewrite ${(2 x - 7 y + 7 z)}^{2}$ as $(2 x - 7 y + 7 z) (2 x - 7 y + 7 z)$ .

$(2 x - 7 y + 7 z) (2 x - 7 y + 7 z)$

Step 2

Expand $(2 x - 7 y + 7 z) (2 x - 7 y + 7 z)$ by multiplying each term in the first expression by each term in the second expression.

$2 x (2 x) + 2 x (- 7 y) + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Step 3

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (- 7 y) + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (- 7 y) + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x (- 7 y) + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x (- 7 y) + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 \cdot - 7 x y + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $2$ by $- 7$ .

$4 x^{2} - 14 x y + 2 x (7 z) - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 2 \cdot 7 x z - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $2$ by $7$ .

$4 x^{2} - 14 x y + 14 x z - 7 y (2 x) - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 14 x z - 7 \cdot 2 y x - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $- 7$ by $2$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x - 7 y (- 7 y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 14 x z - 14 y x - 7 \cdot - 7 y \cdot y - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

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

Move $y$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x - 7 \cdot - 7 (y \cdot y) - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $y$ by $y$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x - 7 \cdot - 7 y^{2} - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $- 7$ by $- 7$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 7 y (7 z) + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 7 \cdot 7 y z + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Multiply $- 7$ by $7$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 7 z (2 x) + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 7 \cdot 2 z x + 7 z (- 7 y) + 7 z (7 z)$

Multiply $7$ by $2$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x + 7 z (- 7 y) + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x + 7 \cdot - 7 z y + 7 z (7 z)$

Multiply $7$ by $- 7$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x - 49 z y + 7 z (7 z)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x - 49 z y + 7 \cdot 7 z \cdot z$

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

Move $z$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x - 49 z y + 7 \cdot 7 (z \cdot z)$

Multiply $z$ by $z$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x - 49 z y + 7 \cdot 7 z^{2}$

Multiply $7$ by $7$ .

$4 x^{2} - 14 x y + 14 x z - 14 y x + 49 y^{2} - 49 y z + 14 z x - 49 z y + 49 z^{2}$

Step 4

Subtract $14 y x$ from $- 14 x y$ .

Move $y$ .

$4 x^{2} - 14 x y - 14 x y + 14 x z + 49 y^{2} - 49 y z + 14 z x - 49 z y + 49 z^{2}$

Subtract $14 x y$ from $- 14 x y$ .

$4 x^{2} - 28 x y + 14 x z + 49 y^{2} - 49 y z + 14 z x - 49 z y + 49 z^{2}$

Step 5

Add $14 x z$ and $14 z x$ .

Move $z$ .

$4 x^{2} - 28 x y + 49 y^{2} - 49 y z + 14 x z + 14 x z - 49 z y + 49 z^{2}$

Add $14 x z$ and $14 x z$ .

$4 x^{2} - 28 x y + 49 y^{2} - 49 y z + 28 x z - 49 z y + 49 z^{2}$

Step 6

Subtract $49 z y$ from $- 49 y z$ .

Move $z$ .

$4 x^{2} - 28 x y + 49 y^{2} - 49 y z - 49 y z + 28 x z + 49 z^{2}$

Subtract $49 y z$ from $- 49 y z$ .

$4 x^{2} - 28 x y + 49 y^{2} - 98 y z + 28 x z + 49 z^{2}$

Expand the Trigonometric Expression (2x-7y+7z)^2

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