Algebra Examples

$(6 - 5 x^{2}) (x^{4} - x^{3})$

Step 1

Expand $(6 - 5 x^{2}) (x^{4} - x^{3})$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$6 (x^{4} - x^{3}) - 5 x^{2} (x^{4} - x^{3})$

Step 1.2

Apply the distributive property.

$6 x^{4} + 6 (- x^{3}) - 5 x^{2} (x^{4} - x^{3})$

Step 1.3

Apply the distributive property.

$6 x^{4} + 6 (- x^{3}) - 5 x^{2} x^{4} - 5 x^{2} (- x^{3})$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $- 1$ by $6$ .

$6 x^{4} - 6 x^{3} - 5 x^{2} x^{4} - 5 x^{2} (- x^{3})$

Step 2.1.2

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Tap for more steps...

Step 2.1.2.1

Move $x^{4}$ .

$6 x^{4} - 6 x^{3} - 5 (x^{4} x^{2}) - 5 x^{2} (- x^{3})$

Step 2.1.2.2

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

$6 x^{4} - 6 x^{3} - 5 x^{4 + 2} - 5 x^{2} (- x^{3})$

Step 2.1.2.3

Add $4$ and $2$ .

$6 x^{4} - 6 x^{3} - 5 x^{6} - 5 x^{2} (- x^{3})$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$6 x^{4} - 6 x^{3} - 5 x^{6} - 5 \cdot - 1 x^{2} x^{3}$

Step 2.1.4

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

Tap for more steps...

Step 2.1.4.1

Move $x^{3}$ .

$6 x^{4} - 6 x^{3} - 5 x^{6} - 5 \cdot - 1 (x^{3} x^{2})$

Step 2.1.4.2

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

$6 x^{4} - 6 x^{3} - 5 x^{6} - 5 \cdot - 1 x^{3 + 2}$

Step 2.1.4.3

Add $3$ and $2$ .

$6 x^{4} - 6 x^{3} - 5 x^{6} - 5 \cdot - 1 x^{5}$

Step 2.1.5

Multiply $- 5$ by $- 1$ .

$6 x^{4} - 6 x^{3} - 5 x^{6} + 5 x^{5}$

Step 2.2

Reorder.

Tap for more steps...

Step 2.2.1

Move $- 6 x^{3}$ .

$6 x^{4} - 5 x^{6} + 5 x^{5} - 6 x^{3}$

Step 2.2.2

Move $6 x^{4}$ .

$- 5 x^{6} + 5 x^{5} + 6 x^{4} - 6 x^{3}$