Finite Math Examples

$(a^{2} b^{2} + 2 a b - 4) - (a^{2} b^{2} - 4 a b + 5)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$a^{2} b^{2} + 2 a b - 4 - (a^{2} b^{2}) - (- 4 a b) - 1 \cdot 5$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 4$ by $- 1$ .

$a^{2} b^{2} + 2 a b - 4 - a^{2} b^{2} + 4 (a b) - 1 \cdot 5$

Step 1.2.2

Multiply $- 1$ by $5$ .

$a^{2} b^{2} + 2 a b - 4 - a^{2} b^{2} + 4 (a b) - 5$

$a^{2} b^{2} + 2 a b - 4 - a^{2} b^{2} + 4 a b - 5$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $a^{2} b^{2} + 2 a b - 4 - a^{2} b^{2} + 4 a b - 5$ .

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Step 2.1.1

Subtract $a^{2} b^{2}$ from $a^{2} b^{2}$ .

$2 a b - 4 + 0 + 4 a b - 5$

Step 2.1.2

Add $2 a b - 4$ and $0$ .

$2 a b - 4 + 4 a b - 5$

Step 2.2

Add $2 a b$ and $4 a b$ .

$6 a b - 4 - 5$

Step 2.3

Subtract $5$ from $- 4$ .

$6 a b - 9$