Basic Math Examples

$3 a \cdot (b - 7) - (5 b - 8) \cdot (3 a - 9) - 3 a$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 a b + 3 a \cdot - 7 - (5 b - 8) \cdot (3 a - 9) - 3 a$

Step 1.2

Multiply $- 7$ by $3$ .

$3 a b - 21 a - (5 b - 8) \cdot (3 a - 9) - 3 a$

Step 1.3

Apply the distributive property.

$3 a b - 21 a + (- (5 b) - - 8) \cdot (3 a - 9) - 3 a$

Step 1.4

Multiply $5$ by $- 1$ .

$3 a b - 21 a + (- 5 b - - 8) \cdot (3 a - 9) - 3 a$

Step 1.5

Multiply $- 1$ by $- 8$ .

$3 a b - 21 a + (- 5 b + 8) \cdot (3 a - 9) - 3 a$

Step 1.6

Expand $(- 5 b + 8) (3 a - 9)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

$3 a b - 21 a - 5 b (3 a - 9) + 8 (3 a - 9) - 3 a$

Step 1.6.2

Apply the distributive property.

$3 a b - 21 a - 5 b (3 a) - 5 b \cdot - 9 + 8 (3 a - 9) - 3 a$

Step 1.6.3

Apply the distributive property.

$3 a b - 21 a - 5 b (3 a) - 5 b \cdot - 9 + 8 (3 a) + 8 \cdot - 9 - 3 a$

Step 1.7

Simplify each term.

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Step 1.7.1

Rewrite using the commutative property of multiplication.

$3 a b - 21 a - 5 \cdot 3 b a - 5 b \cdot - 9 + 8 (3 a) + 8 \cdot - 9 - 3 a$

Step 1.7.2

Multiply $- 5$ by $3$ .

$3 a b - 21 a - 15 b a - 5 b \cdot - 9 + 8 (3 a) + 8 \cdot - 9 - 3 a$

Step 1.7.3

Multiply $- 9$ by $- 5$ .

$3 a b - 21 a - 15 b a + 45 b + 8 (3 a) + 8 \cdot - 9 - 3 a$

Step 1.7.4

Multiply $3$ by $8$ .

$3 a b - 21 a - 15 b a + 45 b + 24 a + 8 \cdot - 9 - 3 a$

Step 1.7.5

Multiply $8$ by $- 9$ .

$3 a b - 21 a - 15 b a + 45 b + 24 a - 72 - 3 a$

Step 2

Subtract $15 b a$ from $3 a b$ .

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Step 2.1

Move $b$ .

$- 21 a + 3 a b - 15 a b + 45 b + 24 a - 72 - 3 a$

Step 2.2

Subtract $15 a b$ from $3 a b$ .

$- 21 a - 12 a b + 45 b + 24 a - 72 - 3 a$

Step 3

Add $- 21 a$ and $24 a$ .

$3 a - 12 a b + 45 b - 72 - 3 a$

Step 4

Combine the opposite terms in $3 a - 12 a b + 45 b - 72 - 3 a$ .

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Step 4.1

Subtract $3 a$ from $3 a$ .

$- 12 a b + 45 b - 72 + 0$

Step 4.2

Add $- 12 a b + 45 b - 72$ and $0$ .

$- 12 a b + 45 b - 72$