Pre-Algebra Examples

$3 b (a + 5) - a (3 - b) + 5 (a + b - 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$3 b a + 3 b \cdot 5 - a (3 - b) + 5 (a + b - 5)$

Step 1.2

Multiply $5$ by $3$ .

$3 b a + 15 b - a (3 - b) + 5 (a + b - 5)$

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $3$ by $- 1$ .

$3 b a + 15 b - 3 a - a (- b) + 5 (a + b - 5)$

Step 1.5

Rewrite using the commutative property of multiplication.

$3 b a + 15 b - 3 a - 1 \cdot - 1 a b + 5 (a + b - 5)$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$3 b a + 15 b - 3 a + 1 a b + 5 (a + b - 5)$

Step 1.6.2

Multiply $a$ by $1$ .

$3 b a + 15 b - 3 a + a b + 5 (a + b - 5)$

Step 1.7

Apply the distributive property.

$3 b a + 15 b - 3 a + a b + 5 a + 5 b + 5 \cdot - 5$

Step 1.8

Multiply $5$ by $- 5$ .

$3 b a + 15 b - 3 a + a b + 5 a + 5 b - 25$

Step 2

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

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Step 2.1

Move $b$ .

$15 b - 3 a + 3 a b + a b + 5 a + 5 b - 25$

Step 2.2

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

$15 b - 3 a + 4 a b + 5 a + 5 b - 25$

Step 3

Add $15 b$ and $5 b$ .

$- 3 a + 4 a b + 5 a + 20 b - 25$

Step 4

Add $- 3 a$ and $5 a$ .

$2 a + 4 a b + 20 b - 25$

Step 5

Reorder $2 a$ and $4 a b$ .

$4 a b + 2 a + 20 b - 25$