Calculus Examples

$- 4 b (7 a - 5 b) + 5 (- 3 a b - 8 b^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 4 b (7 a) - 4 b (- 5 b) + 5 (- 3 a b - 8 b^{2})$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 4 \cdot 7 b a - 4 b (- 5 b) + 5 (- 3 a b - 8 b^{2})$

Step 1.3

Rewrite using the commutative property of multiplication.

$- 4 \cdot 7 b a - 4 \cdot - 5 b \cdot b + 5 (- 3 a b - 8 b^{2})$

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $- 4$ by $7$ .

$- 28 b a - 4 \cdot - 5 b \cdot b + 5 (- 3 a b - 8 b^{2})$

Step 1.4.2

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

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Step 1.4.2.1

Move $b$ .

$- 28 b a - 4 \cdot - 5 (b \cdot b) + 5 (- 3 a b - 8 b^{2})$

Step 1.4.2.2

Multiply $b$ by $b$ .

$- 28 b a - 4 \cdot - 5 b^{2} + 5 (- 3 a b - 8 b^{2})$

Step 1.4.3

Multiply $- 4$ by $- 5$ .

$- 28 b a + 20 b^{2} + 5 (- 3 a b - 8 b^{2})$

Step 1.5

Apply the distributive property.

$- 28 b a + 20 b^{2} + 5 (- 3 a b) + 5 (- 8 b^{2})$

Step 1.6

Multiply $- 3$ by $5$ .

$- 28 b a + 20 b^{2} - 15 (a b) + 5 (- 8 b^{2})$

Step 1.7

Multiply $- 8$ by $5$ .

$- 28 b a + 20 b^{2} - 15 a b - 40 b^{2}$

Step 2

Subtract $15 a b$ from $- 28 b a$ .

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Step 2.1

Move $b$ .

$20 b^{2} - 28 a b - 15 a b - 40 b^{2}$

Step 2.2

Subtract $15 a b$ from $- 28 a b$ .

$20 b^{2} - 43 a b - 40 b^{2}$

Step 3

Subtract $40 b^{2}$ from $20 b^{2}$ .

$- 20 b^{2} - 43 a b$