Expand the Trigonometric Expression (5x-2y^3)^2

${(5 x - 2 y^{3})}^{2}$

Step 1

Rewrite ${(5 x - 2 y^{3})}^{2}$ as $(5 x - 2 y^{3}) (5 x - 2 y^{3})$ .

$(5 x - 2 y^{3}) (5 x - 2 y^{3})$

Step 2

Expand $(5 x - 2 y^{3}) (5 x - 2 y^{3})$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x - 2 y^{3}) - 2 y^{3} (5 x - 2 y^{3})$

Apply the distributive property.

$5 x (5 x) + 5 x (- 2 y^{3}) - 2 y^{3} (5 x - 2 y^{3})$

Apply the distributive property.

$5 x (5 x) + 5 x (- 2 y^{3}) - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x (- 2 y^{3}) - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x (- 2 y^{3}) - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x (- 2 y^{3}) - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

Multiply $5$ by $5$ .

$25 x^{2} + 5 x (- 2 y^{3}) - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

Rewrite using the commutative property of multiplication.

$25 x^{2} + 5 \cdot - 2 x y^{3} - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

Multiply $5$ by $- 2$ .

$25 x^{2} - 10 x y^{3} - 2 y^{3} (5 x) - 2 y^{3} (- 2 y^{3})$

Rewrite using the commutative property of multiplication.

$25 x^{2} - 10 x y^{3} - 2 \cdot 5 y^{3} x - 2 y^{3} (- 2 y^{3})$

Multiply $- 2$ by $5$ .

$25 x^{2} - 10 x y^{3} - 10 y^{3} x - 2 y^{3} (- 2 y^{3})$

Rewrite using the commutative property of multiplication.

$25 x^{2} - 10 x y^{3} - 10 y^{3} x - 2 \cdot - 2 y^{3} y^{3}$

Multiply $y^{3}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$25 x^{2} - 10 x y^{3} - 10 y^{3} x - 2 \cdot - 2 (y^{3} y^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$25 x^{2} - 10 x y^{3} - 10 y^{3} x - 2 \cdot - 2 y^{3 + 3}$

Add $3$ and $3$ .

$25 x^{2} - 10 x y^{3} - 10 y^{3} x - 2 \cdot - 2 y^{6}$

Multiply $- 2$ by $- 2$ .

$25 x^{2} - 10 x y^{3} - 10 y^{3} x + 4 y^{6}$

Subtract $10 y^{3} x$ from $- 10 x y^{3}$ .

Move $y^{3}$ .

$25 x^{2} - 10 x y^{3} - 10 x y^{3} + 4 y^{6}$

Subtract $10 x y^{3}$ from $- 10 x y^{3}$ .

$25 x^{2} - 20 x y^{3} + 4 y^{6}$

Expand the Trigonometric Expression (5x-2y^3)^2

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