Basic Math Examples

$- 5 a (a - b - 1) - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 5 a \cdot a - 5 a (- b) - 5 a \cdot - 1 - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $a$ by $a$ by adding the exponents.

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Step 1.2.1.1

Move $a$ .

$- 5 (a \cdot a) - 5 a (- b) - 5 a \cdot - 1 - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1.2.1.2

Multiply $a$ by $a$ .

$- 5 a^{2} - 5 a (- b) - 5 a \cdot - 1 - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$- 5 a^{2} - 5 \cdot - 1 a b - 5 a \cdot - 1 - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1.2.3

Multiply $- 1$ by $- 5$ .

$- 5 a^{2} - 5 \cdot - 1 a b + 5 a - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1.3

Multiply $- 5$ by $- 1$ .

$- 5 a^{2} + 5 a b + 5 a - 6 (- 7 a + 2 b) + b (a + 8 b - 16)$

Step 1.4

Apply the distributive property.

$- 5 a^{2} + 5 a b + 5 a - 6 (- 7 a) - 6 (2 b) + b (a + 8 b - 16)$

Step 1.5

Multiply $- 7$ by $- 6$ .

$- 5 a^{2} + 5 a b + 5 a + 42 a - 6 (2 b) + b (a + 8 b - 16)$

Step 1.6

Multiply $2$ by $- 6$ .

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b (a + 8 b - 16)$

Step 1.7

Apply the distributive property.

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b a + b (8 b) + b \cdot - 16$

Step 1.8

Simplify.

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Step 1.8.1

Rewrite using the commutative property of multiplication.

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b a + 8 b \cdot b + b \cdot - 16$

Step 1.8.2

Move $- 16$ to the left of $b$ .

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b a + 8 b \cdot b - 16 \cdot b$

Step 1.9

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

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Step 1.9.1

Move $b$ .

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b a + 8 (b \cdot b) - 16 \cdot b$

Step 1.9.2

Multiply $b$ by $b$ .

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b a + 8 b^{2} - 16 \cdot b$

$- 5 a^{2} + 5 a b + 5 a + 42 a - 12 b + b a + 8 b^{2} - 16 b$

Step 2

Add $5 a b$ and $b a$ .

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Step 2.1

Reorder $b$ and $a$ .

$- 5 a^{2} + 5 a + 42 a - 12 b + 5 a b + a b + 8 b^{2} - 16 b$

Step 2.2

Add $5 a b$ and $a b$ .

$- 5 a^{2} + 5 a + 42 a - 12 b + 6 a b + 8 b^{2} - 16 b$

Step 3

Add $5 a$ and $42 a$ .

$- 5 a^{2} + 47 a - 12 b + 6 a b + 8 b^{2} - 16 b$

Step 4

Subtract $16 b$ from $- 12 b$ .

$- 5 a^{2} + 47 a - 28 b + 6 a b + 8 b^{2}$

Step 5

Reorder.

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Step 5.1

Move $- 28 b$ .

$- 5 a^{2} + 47 a + 6 a b + 8 b^{2} - 28 b$

Step 5.2

Move $47 a$ .

$- 5 a^{2} + 6 a b + 8 b^{2} + 47 a - 28 b$