Algebra Examples

$4 k^{2} (6 k^{2} + 9 k q - 5 q^{2})$

Step 1

Apply the distributive property.

$4 k^{2} (6 k^{2}) + 4 k^{2} (9 k q) + 4 k^{2} (- 5 q^{2})$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 6 k^{2} k^{2} + 4 k^{2} (9 k q) + 4 k^{2} (- 5 q^{2})$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Move $k$ .

$4 \cdot 6 k^{2} k^{2} + 4 (k \cdot k^{2}) (9 q) + 4 k^{2} (- 5 q^{2})$

Step 2.2.2

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

Tap for more steps...

Step 2.2.2.1

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

$4 \cdot 6 k^{2} k^{2} + 4 (k^{1} k^{2}) (9 q) + 4 k^{2} (- 5 q^{2})$

Step 2.2.2.2

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

$4 \cdot 6 k^{2} k^{2} + 4 k^{1 + 2} (9 q) + 4 k^{2} (- 5 q^{2})$

Step 2.2.3

Add $1$ and $2$ .

$4 \cdot 6 k^{2} k^{2} + 4 k^{3} (9 q) + 4 k^{2} (- 5 q^{2})$

Step 2.3

Rewrite using the commutative property of multiplication.

$4 \cdot 6 k^{2} k^{2} + 4 k^{3} (9 q) + 4 \cdot - 5 k^{2} q^{2}$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Move $k^{2}$ .

$4 \cdot 6 (k^{2} k^{2}) + 4 k^{3} (9 q) + 4 \cdot - 5 k^{2} q^{2}$

Step 3.1.2

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

$4 \cdot 6 k^{2 + 2} + 4 k^{3} (9 q) + 4 \cdot - 5 k^{2} q^{2}$

Step 3.1.3

Add $2$ and $2$ .

$4 \cdot 6 k^{4} + 4 k^{3} (9 q) + 4 \cdot - 5 k^{2} q^{2}$

Step 3.2

Multiply $4$ by $6$ .

$24 k^{4} + 4 k^{3} (9 q) + 4 \cdot - 5 k^{2} q^{2}$

Step 3.3

Rewrite using the commutative property of multiplication.

$24 k^{4} + 4 \cdot 9 k^{3} q + 4 \cdot - 5 k^{2} q^{2}$

Step 3.4

Multiply $4$ by $9$ .

$24 k^{4} + 36 k^{3} q + 4 \cdot - 5 k^{2} q^{2}$

Step 3.5

Multiply $4$ by $- 5$ .

$24 k^{4} + 36 k^{3} q - 20 k^{2} q^{2}$