Algebra Examples

$(2 f^{4} - 5 f^{3} - 3 f^{2}) - (4 f^{4} - 3 f^{3} - f^{2} - 4 f)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 f^{4} - 5 f^{3} - 3 f^{2} - (4 f^{4}) - (- 3 f^{3}) - - f^{2} - (- 4 f)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $4$ by $- 1$ .

$2 f^{4} - 5 f^{3} - 3 f^{2} - 4 f^{4} - (- 3 f^{3}) - - f^{2} - (- 4 f)$

Step 1.2.2

Multiply $- 3$ by $- 1$ .

$2 f^{4} - 5 f^{3} - 3 f^{2} - 4 f^{4} + 3 f^{3} - - f^{2} - (- 4 f)$

Step 1.2.3

Multiply $- - f^{2}$ .

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Step 1.2.3.1

Multiply $- 1$ by $- 1$ .

$2 f^{4} - 5 f^{3} - 3 f^{2} - 4 f^{4} + 3 f^{3} + 1 f^{2} - (- 4 f)$

Step 1.2.3.2

Multiply $f^{2}$ by $1$ .

$2 f^{4} - 5 f^{3} - 3 f^{2} - 4 f^{4} + 3 f^{3} + f^{2} - (- 4 f)$

Step 1.2.4

Multiply $- 4$ by $- 1$ .

$2 f^{4} - 5 f^{3} - 3 f^{2} - 4 f^{4} + 3 f^{3} + f^{2} + 4 f$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $4 f^{4}$ from $2 f^{4}$ .

$- 2 f^{4} - 5 f^{3} - 3 f^{2} + 3 f^{3} + f^{2} + 4 f$

Step 2.2

Add $- 5 f^{3}$ and $3 f^{3}$ .

$- 2 f^{4} - 2 f^{3} - 3 f^{2} + f^{2} + 4 f$

Step 2.3

Add $- 3 f^{2}$ and $f^{2}$ .

$- 2 f^{4} - 2 f^{3} - 2 f^{2} + 4 f$