Algebra Examples

$(- 2 x^{3}) \cdot (x^{7} - x^{2} y^{2})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Apply the distributive property.

$- 2 x^{3} x^{7} - 2 x^{3} (- x^{2} y^{2})$

Step 1.2

Multiply $x^{3}$ by $x^{7}$ by adding the exponents.

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Step 1.2.1

Move $x^{7}$ .

$- 2 (x^{7} x^{3}) - 2 x^{3} (- x^{2} y^{2})$

Step 1.2.2

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

$- 2 x^{7 + 3} - 2 x^{3} (- x^{2} y^{2})$

Step 1.2.3

Add $7$ and $3$ .

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

Step 1.3

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Step 1.3.1

Move $x^{2}$ .

$- 2 x^{10} - 2 (x^{2} x^{3}) (- 1 y^{2})$

Step 1.3.2

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

$- 2 x^{10} - 2 x^{2 + 3} (- 1 y^{2})$

Step 1.3.3

Add $2$ and $3$ .

$- 2 x^{10} - 2 x^{5} (- 1 y^{2})$

Step 1.4

Simplify each term.

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Step 1.4.1

Rewrite using the commutative property of multiplication.

$- 2 x^{10} - 2 \cdot - 1 x^{5} y^{2}$

Step 1.4.2

Multiply $- 2$ by $- 1$ .

$- 2 x^{10} + 2 x^{5} y^{2}$

Step 2

The largest exponent is the degree of the polynomial.

$10$