Algebra Examples

$- 3 a (a + b - 5) + 4 (- 2 a + 2 b) + b (a + 3 b - 7)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 3 a \cdot a - 3 a b - 3 a \cdot - 5 + 4 (- 2 a + 2 b) + b (a + 3 b - 7)$

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 $a$ .

$- 3 (a \cdot a) - 3 a b - 3 a \cdot - 5 + 4 (- 2 a + 2 b) + b (a + 3 b - 7)$

Step 1.2.1.2

Multiply $a$ by $a$ .

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

Step 1.2.2

Multiply $- 5$ by $- 3$ .

$- 3 a^{2} - 3 a b + 15 a + 4 (- 2 a + 2 b) + b (a + 3 b - 7)$

Step 1.3

Apply the distributive property.

$- 3 a^{2} - 3 a b + 15 a + 4 (- 2 a) + 4 (2 b) + b (a + 3 b - 7)$

Step 1.4

Multiply $- 2$ by $4$ .

$- 3 a^{2} - 3 a b + 15 a - 8 a + 4 (2 b) + b (a + 3 b - 7)$

Step 1.5

Multiply $2$ by $4$ .

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b (a + 3 b - 7)$

Step 1.6

Apply the distributive property.

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b a + b (3 b) + b \cdot - 7$

Step 1.7

Simplify.

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Step 1.7.1

Rewrite using the commutative property of multiplication.

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b a + 3 b \cdot b + b \cdot - 7$

Step 1.7.2

Move $- 7$ to the left of $b$ .

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b a + 3 b \cdot b - 7 \cdot b$

Step 1.8

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

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Step 1.8.1

Move $b$ .

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b a + 3 (b \cdot b) - 7 \cdot b$

Step 1.8.2

Multiply $b$ by $b$ .

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b a + 3 b^{2} - 7 \cdot b$

$- 3 a^{2} - 3 a b + 15 a - 8 a + 8 b + b a + 3 b^{2} - 7 b$

Step 2

Add $- 3 a b$ and $b a$ .

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Step 2.1

Reorder $b$ and $a$ .

$- 3 a^{2} + 15 a - 8 a + 8 b - 3 a b + a b + 3 b^{2} - 7 b$

Step 2.2

Add $- 3 a b$ and $a b$ .

$- 3 a^{2} + 15 a - 8 a + 8 b - 2 a b + 3 b^{2} - 7 b$

Step 3

Subtract $8 a$ from $15 a$ .

$- 3 a^{2} + 7 a + 8 b - 2 a b + 3 b^{2} - 7 b$

Step 4

Subtract $7 b$ from $8 b$ .

$- 3 a^{2} + 7 a + b - 2 a b + 3 b^{2}$

Step 5

Reorder.

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Step 5.1

Move $b$ .

$- 3 a^{2} + 7 a - 2 a b + 3 b^{2} + b$

Step 5.2

Move $7 a$ .

$- 3 a^{2} - 2 a b + 3 b^{2} + 7 a + b$