Basic Math Examples

$5 b (1 + 6 b) - 5 b (8 b + 7)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 b \cdot 1 + 5 b (6 b) - 5 b (8 b + 7)$

Step 1.2

Multiply $5$ by $1$ .

$5 b + 5 b (6 b) - 5 b (8 b + 7)$

Step 1.3

Rewrite using the commutative property of multiplication.

$5 b + 5 \cdot 6 b \cdot b - 5 b (8 b + 7)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $b$ .

$5 b + 5 \cdot 6 (b \cdot b) - 5 b (8 b + 7)$

Step 1.4.1.2

Multiply $b$ by $b$ .

$5 b + 5 \cdot 6 b^{2} - 5 b (8 b + 7)$

Step 1.4.2

Multiply $5$ by $6$ .

$5 b + 30 b^{2} - 5 b (8 b + 7)$

Step 1.5

Apply the distributive property.

$5 b + 30 b^{2} - 5 b (8 b) - 5 b \cdot 7$

Step 1.6

Rewrite using the commutative property of multiplication.

$5 b + 30 b^{2} - 5 \cdot 8 b \cdot b - 5 b \cdot 7$

Step 1.7

Multiply $7$ by $- 5$ .

$5 b + 30 b^{2} - 5 \cdot 8 b \cdot b - 35 b$

Step 1.8

Simplify each term.

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Step 1.8.1

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

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Step 1.8.1.1

Move $b$ .

$5 b + 30 b^{2} - 5 \cdot 8 (b \cdot b) - 35 b$

Step 1.8.1.2

Multiply $b$ by $b$ .

$5 b + 30 b^{2} - 5 \cdot 8 b^{2} - 35 b$

Step 1.8.2

Multiply $- 5$ by $8$ .

$5 b + 30 b^{2} - 40 b^{2} - 35 b$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $35 b$ from $5 b$ .

$30 b^{2} - 40 b^{2} - 30 b$

Step 2.2

Subtract $40 b^{2}$ from $30 b^{2}$ .

$- 10 b^{2} - 30 b$