Algebra Examples

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

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

Expand $(3 x - y) (x^{2} - 2)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

$3 x \cdot x^{2} + 3 x \cdot - 2 - y x^{2} - y \cdot - 2 + x^{2} - 2$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Move $x^{2}$ .

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

Step 3.1.2

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 3.1.2.1

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

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

Step 3.1.2.2

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

$3 x^{2 + 1} + 3 x \cdot - 2 - y x^{2} - y \cdot - 2 + x^{2} - 2$

Step 3.1.3

Add $2$ and $1$ .

$3 x^{3} + 3 x \cdot - 2 - y x^{2} - y \cdot - 2 + x^{2} - 2$

Step 3.2

Multiply $- 2$ by $3$ .

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

Step 3.3

Multiply $- 2$ by $- 1$ .

$3 x^{3} - 6 x - y x^{2} + 2 y + x^{2} - 2$