Basic Math Examples

$- 2 (3 k - 5) (5 - 3 k)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$(- 2 (3 k) - 2 \cdot - 5) (5 - 3 k)$

Step 1.2

Multiply.

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Step 1.2.1

Multiply $3$ by $- 2$ .

$(- 6 k - 2 \cdot - 5) (5 - 3 k)$

Step 1.2.2

Multiply $- 2$ by $- 5$ .

$(- 6 k + 10) (5 - 3 k)$

Step 2

Expand $(- 6 k + 10) (5 - 3 k)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 6 k (5 - 3 k) + 10 (5 - 3 k)$

Step 2.2

Apply the distributive property.

$- 6 k \cdot 5 - 6 k (- 3 k) + 10 (5 - 3 k)$

Step 2.3

Apply the distributive property.

$- 6 k \cdot 5 - 6 k (- 3 k) + 10 \cdot 5 + 10 (- 3 k)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $5$ by $- 6$ .

$- 30 k - 6 k (- 3 k) + 10 \cdot 5 + 10 (- 3 k)$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$- 30 k - 6 \cdot - 3 k \cdot k + 10 \cdot 5 + 10 (- 3 k)$

Step 3.1.3

Multiply $k$ by $k$ by adding the exponents.

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Step 3.1.3.1

Move $k$ .

$- 30 k - 6 \cdot - 3 (k \cdot k) + 10 \cdot 5 + 10 (- 3 k)$

Step 3.1.3.2

Multiply $k$ by $k$ .

$- 30 k - 6 \cdot - 3 k^{2} + 10 \cdot 5 + 10 (- 3 k)$

Step 3.1.4

Multiply $- 6$ by $- 3$ .

$- 30 k + 18 k^{2} + 10 \cdot 5 + 10 (- 3 k)$

Step 3.1.5

Multiply $10$ by $5$ .

$- 30 k + 18 k^{2} + 50 + 10 (- 3 k)$

Step 3.1.6

Multiply $- 3$ by $10$ .

$- 30 k + 18 k^{2} + 50 - 30 k$

Step 3.2

Subtract $30 k$ from $- 30 k$ .

$- 60 k + 18 k^{2} + 50$

Step 4

Reorder $- 60 k$ and $18 k^{2}$ .

$18 k^{2} - 60 k + 50$