Calculus Examples

$(8 x^{2} - 3 x^{3}) (5 x^{2} - 8 x^{3})$

Step 1

Factor $x^{2}$ out of $8 x^{2} - 3 x^{3}$ .

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Step 1.1

Factor $x^{2}$ out of $8 x^{2}$ .

$(x^{2} \cdot 8 - 3 x^{3}) (5 x^{2} - 8 x^{3})$

Step 1.2

Factor $x^{2}$ out of $- 3 x^{3}$ .

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

Step 1.3

Factor $x^{2}$ out of $x^{2} \cdot 8 + x^{2} (- 3 x)$ .

$x^{2} (8 - 3 x) (5 x^{2} - 8 x^{3})$

Step 2

Factor.

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Step 2.1

Factor $x^{2}$ out of $5 x^{2} - 8 x^{3}$ .

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Step 2.1.1

Factor $x^{2}$ out of $5 x^{2}$ .

$x^{2} (8 - 3 x) (x^{2} \cdot 5 - 8 x^{3})$

Step 2.1.2

Factor $x^{2}$ out of $- 8 x^{3}$ .

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

Step 2.1.3

Factor $x^{2}$ out of $x^{2} \cdot 5 + x^{2} (- 8 x)$ .

$x^{2} (8 - 3 x) (x^{2} (5 - 8 x))$

Step 2.2

Remove unnecessary parentheses.

$x^{2} (8 - 3 x) x^{2} (5 - 8 x)$

Step 3

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

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Step 3.1

Move $x^{2}$ .

$x^{2} x^{2} (8 - 3 x) (5 - 8 x)$

Step 3.2

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

$x^{2 + 2} (8 - 3 x) (5 - 8 x)$

Step 3.3

Add $2$ and $2$ .

$x^{4} (8 - 3 x) (5 - 8 x)$