Basic Math Examples

$(12 r^{4} - 7 r^{3} + 2 r^{2}) - (5 r^{4} - 3 r^{3} + 2 r^{2} + 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$12 r^{4} - 7 r^{3} + 2 r^{2} - (5 r^{4}) - (- 3 r^{3}) - (2 r^{2}) - 1 \cdot 1$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $5$ by $- 1$ .

$12 r^{4} - 7 r^{3} + 2 r^{2} - 5 r^{4} - (- 3 r^{3}) - (2 r^{2}) - 1 \cdot 1$

Step 1.2.2

Multiply $- 3$ by $- 1$ .

$12 r^{4} - 7 r^{3} + 2 r^{2} - 5 r^{4} + 3 r^{3} - (2 r^{2}) - 1 \cdot 1$

Step 1.2.3

Multiply $2$ by $- 1$ .

$12 r^{4} - 7 r^{3} + 2 r^{2} - 5 r^{4} + 3 r^{3} - 2 r^{2} - 1 \cdot 1$

Step 1.2.4

Multiply $- 1$ by $1$ .

$12 r^{4} - 7 r^{3} + 2 r^{2} - 5 r^{4} + 3 r^{3} - 2 r^{2} - 1$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $12 r^{4} - 7 r^{3} + 2 r^{2} - 5 r^{4} + 3 r^{3} - 2 r^{2} - 1$ .

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Step 2.1.1

Subtract $2 r^{2}$ from $2 r^{2}$ .

$12 r^{4} - 7 r^{3} - 5 r^{4} + 3 r^{3} + 0 - 1$

Step 2.1.2

Add $12 r^{4} - 7 r^{3} - 5 r^{4} + 3 r^{3}$ and $0$ .

$12 r^{4} - 7 r^{3} - 5 r^{4} + 3 r^{3} - 1$

Step 2.2

Subtract $5 r^{4}$ from $12 r^{4}$ .

$7 r^{4} - 7 r^{3} + 3 r^{3} - 1$

Step 2.3

Add $- 7 r^{3}$ and $3 r^{3}$ .

$7 r^{4} - 4 r^{3} - 1$