Algebra Examples

$(- 8 x^{4} y^{3}) \cdot (2 x^{5} y^{2}) + 7 x^{9} y^{5}$

Step 1

Simplify each term.

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Step 1.1

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

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Step 1.1.1

Move $x^{5}$ .

$- 8 (x^{5} x^{4}) y^{3} \cdot (2 y^{2}) + 7 x^{9} y^{5}$

Step 1.1.2

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

$- 8 x^{5 + 4} y^{3} \cdot (2 y^{2}) + 7 x^{9} y^{5}$

Step 1.1.3

Add $5$ and $4$ .

$- 8 x^{9} y^{3} \cdot (2 y^{2}) + 7 x^{9} y^{5}$

Step 1.2

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

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Step 1.2.1

Move $y^{2}$ .

$- 8 x^{9} (y^{2} y^{3}) \cdot 2 + 7 x^{9} y^{5}$

Step 1.2.2

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

$- 8 x^{9} y^{2 + 3} \cdot 2 + 7 x^{9} y^{5}$

Step 1.2.3

Add $2$ and $3$ .

$- 8 x^{9} y^{5} \cdot 2 + 7 x^{9} y^{5}$

Step 1.3

Multiply $2$ by $- 8$ .

$- 16 x^{9} y^{5} + 7 x^{9} y^{5}$

Step 2

Add $- 16 x^{9} y^{5}$ and $7 x^{9} y^{5}$ .

$- 9 x^{9} y^{5}$