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

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

Step 1

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

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

Step 2

Expand $(7 x - 2 y) (7 x - 2 y)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $7$ by $7$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $7$ by $- 2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 2$ by $7$ .

$49 x^{2} - 14 x y - 14 y x - 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$49 x^{2} - 14 x y - 14 y x - 2 \cdot - 2 y \cdot y$

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

Move $y$ .

$49 x^{2} - 14 x y - 14 y x - 2 \cdot - 2 (y \cdot y)$

Multiply $y$ by $y$ .

$49 x^{2} - 14 x y - 14 y x - 2 \cdot - 2 y^{2}$

Multiply $- 2$ by $- 2$ .

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

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

Move $y$ .

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

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

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

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

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