Pre-Algebra Examples

$(- 2 b^{2}) (4 b^{3}) + (6 b^{3}) (- 3 b^{2})$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$- 2 \cdot 4 b^{2} b^{3} + (6 b^{3}) (- 3 b^{2})$

Step 1.2

Multiply $b^{2}$ by $b^{3}$ by adding the exponents.

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Step 1.2.1

Move $b^{3}$ .

$- 2 \cdot 4 (b^{3} b^{2}) + (6 b^{3}) (- 3 b^{2})$

Step 1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 \cdot 4 b^{3 + 2} + (6 b^{3}) (- 3 b^{2})$

Step 1.2.3

Add $3$ and $2$ .

$- 2 \cdot 4 b^{5} + (6 b^{3}) (- 3 b^{2})$

Step 1.3

Multiply $- 2$ by $4$ .

$- 8 b^{5} + (6 b^{3}) (- 3 b^{2})$

Step 1.4

Rewrite using the commutative property of multiplication.

$- 8 b^{5} + 6 \cdot - 3 b^{3} b^{2}$

Step 1.5

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

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Step 1.5.1

Move $b^{2}$ .

$- 8 b^{5} + 6 \cdot - 3 (b^{2} b^{3})$

Step 1.5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 8 b^{5} + 6 \cdot - 3 b^{2 + 3}$

Step 1.5.3

Add $2$ and $3$ .

$- 8 b^{5} + 6 \cdot - 3 b^{5}$

Step 1.6

Multiply $6$ by $- 3$ .

$- 8 b^{5} - 18 b^{5}$

Step 2

Subtract $18 b^{5}$ from $- 8 b^{5}$ .

$- 26 b^{5}$