Find the Product (10x^3-9xy^5)^2

${(10 x^{3} - 9 x y^{5})}^{2}$

Step 1

Rewrite ${(10 x^{3} - 9 x y^{5})}^{2}$ as $(10 x^{3} - 9 x y^{5}) (10 x^{3} - 9 x y^{5})$ .

$(10 x^{3} - 9 x y^{5}) (10 x^{3} - 9 x y^{5})$

Step 2

Expand $(10 x^{3} - 9 x y^{5}) (10 x^{3} - 9 x y^{5})$ using the FOIL Method.

Apply the distributive property.

$10 x^{3} (10 x^{3} - 9 x y^{5}) - 9 x y^{5} (10 x^{3} - 9 x y^{5})$

Apply the distributive property.

$10 x^{3} (10 x^{3}) + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3} - 9 x y^{5})$

Apply the distributive property.

$10 x^{3} (10 x^{3}) + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$10 \cdot 10 x^{3} x^{3} + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

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

Move $x^{3}$ .

$10 \cdot 10 (x^{3} x^{3}) + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

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

$10 \cdot 10 x^{3 + 3} + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Add $3$ and $3$ .

$10 \cdot 10 x^{6} + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Multiply $10$ by $10$ .

$100 x^{6} + 10 x^{3} (- 9 x y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

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

Move $x$ .

$100 x^{6} + 10 (x \cdot x^{3}) (- 9 y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Multiply $x$ by $x^{3}$ .

Raise $x$ to the power of $1$ .

$100 x^{6} + 10 (x^{1} x^{3}) (- 9 y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

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

$100 x^{6} + 10 x^{1 + 3} (- 9 y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Add $1$ and $3$ .

$100 x^{6} + 10 x^{4} (- 9 y^{5}) - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Rewrite using the commutative property of multiplication.

$100 x^{6} + 10 \cdot - 9 x^{4} y^{5} - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

Multiply $10$ by $- 9$ .

$100 x^{6} - 90 x^{4} y^{5} - 9 x y^{5} (10 x^{3}) - 9 x y^{5} (- 9 x y^{5})$

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

Move $x^{3}$ .

$100 x^{6} - 90 x^{4} y^{5} - 9 (x^{3} x) y^{5} \cdot 10 - 9 x y^{5} (- 9 x y^{5})$

Multiply $x^{3}$ by $x$ .

Raise $x$ to the power of $1$ .

$100 x^{6} - 90 x^{4} y^{5} - 9 (x^{3} x^{1}) y^{5} \cdot 10 - 9 x y^{5} (- 9 x y^{5})$

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

$100 x^{6} - 90 x^{4} y^{5} - 9 x^{3 + 1} y^{5} \cdot 10 - 9 x y^{5} (- 9 x y^{5})$

Add $3$ and $1$ .

$100 x^{6} - 90 x^{4} y^{5} - 9 x^{4} y^{5} \cdot 10 - 9 x y^{5} (- 9 x y^{5})$

Multiply $10$ by $- 9$ .

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} - 9 x y^{5} (- 9 x y^{5})$

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

Move $x$ .

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} - 9 (x \cdot x) y^{5} (- 9 y^{5})$

Multiply $x$ by $x$ .

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} - 9 x^{2} y^{5} (- 9 y^{5})$

Multiply $y^{5}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} - 9 x^{2} (y^{5} y^{5}) \cdot - 9$

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

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} - 9 x^{2} y^{5 + 5} \cdot - 9$

Add $5$ and $5$ .

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} - 9 x^{2} y^{10} \cdot - 9$

Multiply $- 9$ by $- 9$ .

$100 x^{6} - 90 x^{4} y^{5} - 90 x^{4} y^{5} + 81 x^{2} y^{10}$

Subtract $90 x^{4} y^{5}$ from $- 90 x^{4} y^{5}$ .

$100 x^{6} - 180 x^{4} y^{5} + 81 x^{2} y^{10}$

Find the Product (10x^3-9xy^5)^2

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