Algebra Examples

$(4 e^{4} + 7 e^{3} - 9 e^{2} + 4 e) - (- e^{3} + 5 e^{2} - 7 e)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$4 e^{4} + 7 e^{3} - 9 e^{2} + 4 e - - e^{3} - (5 e^{2}) - (- 7 e)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - e^{3}$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

$4 e^{4} + 7 e^{3} - 9 e^{2} + 4 e + 1 e^{3} - (5 e^{2}) - (- 7 e)$

Step 1.2.1.2

Multiply $e^{3}$ by $1$ .

$4 e^{4} + 7 e^{3} - 9 e^{2} + 4 e + e^{3} - (5 e^{2}) - (- 7 e)$

Step 1.2.2

Multiply $5$ by $- 1$ .

$4 e^{4} + 7 e^{3} - 9 e^{2} + 4 e + e^{3} - 5 e^{2} - (- 7 e)$

Step 1.2.3

Multiply $- 7$ by $- 1$ .

$4 e^{4} + 7 e^{3} - 9 e^{2} + 4 e + e^{3} - 5 e^{2} + 7 e$

Step 2

Simplify by adding terms.

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Step 2.1

Add $7 e^{3}$ and $e^{3}$ .

$4 e^{4} + 8 e^{3} - 9 e^{2} + 4 e - 5 e^{2} + 7 e$

Step 2.2

Subtract $5 e^{2}$ from $- 9 e^{2}$ .

$4 e^{4} + 8 e^{3} - 14 e^{2} + 4 e + 7 e$

Step 2.3

Add $4 e$ and $7 e$ .

$4 e^{4} + 8 e^{3} - 14 e^{2} + 11 e$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 e^{4} + 8 e^{3} - 14 e^{2} + 11 e$

Decimal Form:

$305.53121024 \dots$