Basic Math Examples

$- 3 (b^{2} + 2 b) - 5 b (2 b - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 3 b^{2} - 3 (2 b) - 5 b (2 b - 3)$

Step 1.2

Multiply $2$ by $- 3$ .

$- 3 b^{2} - 6 b - 5 b (2 b - 3)$

Step 1.3

Apply the distributive property.

$- 3 b^{2} - 6 b - 5 b (2 b) - 5 b \cdot - 3$

Step 1.4

Rewrite using the commutative property of multiplication.

$- 3 b^{2} - 6 b - 5 \cdot 2 b \cdot b - 5 b \cdot - 3$

Step 1.5

Multiply $- 3$ by $- 5$ .

$- 3 b^{2} - 6 b - 5 \cdot 2 b \cdot b + 15 b$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $b$ by $b$ by adding the exponents.

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Step 1.6.1.1

Move $b$ .

$- 3 b^{2} - 6 b - 5 \cdot 2 (b \cdot b) + 15 b$

Step 1.6.1.2

Multiply $b$ by $b$ .

$- 3 b^{2} - 6 b - 5 \cdot 2 b^{2} + 15 b$

Step 1.6.2

Multiply $- 5$ by $2$ .

$- 3 b^{2} - 6 b - 10 b^{2} + 15 b$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $10 b^{2}$ from $- 3 b^{2}$ .

$- 13 b^{2} - 6 b + 15 b$

Step 2.2

Add $- 6 b$ and $15 b$ .

$- 13 b^{2} + 9 b$