Pre-Algebra Examples

$5 x^{2} y^{3} - 6 x^{2} y^{2} - 8 x^{2} y^{3} + 4 x^{3} y^{2} \cdot (6 x^{2} y^{2})$

Step 1

The polynomial cannot be factored using the grouping method. Try a different method, or if you aren't sure, choose Factor.

The polynomial cannot be factored using the grouping method.

Step 2

Subtract $8 x^{2} y^{3}$ from $5 x^{2} y^{3}$ .

$- 3 x^{2} y^{3} - 6 x^{2} y^{2} + 4 x^{3} y^{2} \cdot (6 x^{2} y^{2})$

Step 3

Factor $x^{2} y^{2}$ out of $- 3 x^{2} y^{3} - 6 x^{2} y^{2} + 4 x^{3} y^{2} \cdot (6 x^{2} y^{2})$ .

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Step 3.1

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

$x^{2} y^{2} (- 3 y) - 6 x^{2} y^{2} + 4 x^{3} y^{2} \cdot (6 x^{2} y^{2})$

Step 3.2

Factor $x^{2} y^{2}$ out of $- 6 x^{2} y^{2}$ .

$x^{2} y^{2} (- 3 y) + x^{2} y^{2} (- 6) + 4 x^{3} y^{2} \cdot (6 x^{2} y^{2})$

Step 3.3

Factor $x^{2} y^{2}$ out of $4 x^{3} y^{2} \cdot (6 x^{2} y^{2})$ .

$x^{2} y^{2} (- 3 y) + x^{2} y^{2} (- 6) + x^{2} y^{2} (4 x \cdot (6 x^{2} y^{2}))$

Step 3.4

Factor $x^{2} y^{2}$ out of $x^{2} y^{2} (- 3 y) + x^{2} y^{2} (- 6)$ .

$x^{2} y^{2} (- 3 y - 6) + x^{2} y^{2} (4 x \cdot (6 x^{2} y^{2}))$

Step 3.5

Factor $x^{2} y^{2}$ out of $x^{2} y^{2} (- 3 y - 6) + x^{2} y^{2} (4 x \cdot (6 x^{2} y^{2}))$ .

$x^{2} y^{2} (- 3 y - 6 + 4 x \cdot (6 x^{2} y^{2}))$

Step 4

Combine exponents.

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Step 4.1

Multiply $6$ by $4$ .

$x^{2} y^{2} (- 3 y - 6 + 24 x \cdot (x^{2} y^{2}))$

Step 4.2

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

$x^{2} y^{2} (- 3 y - 6 + 24 (x^{2} x^{1}) \cdot y^{2})$

Step 4.3

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

$x^{2} y^{2} (- 3 y - 6 + 24 x^{2 + 1} \cdot y^{2})$

Step 4.4

Add $2$ and $1$ .

$x^{2} y^{2} (- 3 y - 6 + 24 x^{3} \cdot y^{2})$