Expand the Trigonometric Expression (x-2y+3x)^2

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

Step 1

Simplify by adding terms.

Add $x$ and $3 x$ .

${(4 x - 2 y)}^{2}$

Rewrite ${(4 x - 2 y)}^{2}$ as $(4 x - 2 y) (4 x - 2 y)$ .

$(4 x - 2 y) (4 x - 2 y)$

Step 2

Expand $(4 x - 2 y) (4 x - 2 y)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 2 y) - 2 y (4 x - 2 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 2 y) - 2 y (4 x - 2 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 2 y) - 2 y (4 x) - 2 y (- 2 y)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x (- 2 y) - 2 y (4 x) - 2 y (- 2 y)$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x (- 2 y) - 2 y (4 x) - 2 y (- 2 y)$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x (- 2 y) - 2 y (4 x) - 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} + 4 \cdot - 2 x y - 2 y (4 x) - 2 y (- 2 y)$

Multiply $4$ by $- 2$ .

$16 x^{2} - 8 x y - 2 y (4 x) - 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 8 x y - 2 \cdot 4 y x - 2 y (- 2 y)$

Multiply $- 2$ by $4$ .

$16 x^{2} - 8 x y - 8 y x - 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 8 x y - 8 y x - 2 \cdot - 2 y \cdot y$

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

Move $y$ .

$16 x^{2} - 8 x y - 8 y x - 2 \cdot - 2 (y \cdot y)$

Multiply $y$ by $y$ .

$16 x^{2} - 8 x y - 8 y x - 2 \cdot - 2 y^{2}$

Multiply $- 2$ by $- 2$ .

$16 x^{2} - 8 x y - 8 y x + 4 y^{2}$

Subtract $8 y x$ from $- 8 x y$ .

Move $y$ .

$16 x^{2} - 8 x y - 8 x y + 4 y^{2}$

Subtract $8 x y$ from $- 8 x y$ .

$16 x^{2} - 16 x y + 4 y^{2}$

Expand the Trigonometric Expression (x-2y+3x)^2

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