Calculus Examples

$(x + 1) \cdot (1 - x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1

Simplify each term.

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Step 1.1

Expand $(x + 1) (1 - x)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

$x \cdot 1 + x (- x) + 1 (1 - x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.1.3

Apply the distributive property.

$x \cdot 1 + x (- x) + 1 \cdot 1 + 1 (- x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $x$ by $1$ .

$x + x (- x) + 1 \cdot 1 + 1 (- x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$x - x \cdot x + 1 \cdot 1 + 1 (- x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.2.1.3

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1.3.1

Move $x$ .

$x - (x \cdot x) + 1 \cdot 1 + 1 (- x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.2.1.3.2

Multiply $x$ by $x$ .

$x - x^{2} + 1 \cdot 1 + 1 (- x) + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.2.1.4

Multiply $1$ by $1$ .

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

Step 1.2.1.5

Multiply $- x$ by $1$ .

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

Step 1.2.2

Subtract $x$ from $x$ .

$- x^{2} + 1 + 0 + 2 (x - 5) - (2 x^{2} - 3)$

Step 1.2.3

Add $- x^{2}$ and $0$ .

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

Step 1.3

Apply the distributive property.

$- x^{2} + 1 + 2 x + 2 \cdot - 5 - (2 x^{2} - 3)$

Step 1.4

Multiply $2$ by $- 5$ .

$- x^{2} + 1 + 2 x - 10 - (2 x^{2} - 3)$

Step 1.5

Apply the distributive property.

$- x^{2} + 1 + 2 x - 10 - (2 x^{2}) - - 3$

Step 1.6

Multiply $2$ by $- 1$ .

$- x^{2} + 1 + 2 x - 10 - 2 x^{2} - - 3$

Step 1.7

Multiply $- 1$ by $- 3$ .

$- x^{2} + 1 + 2 x - 10 - 2 x^{2} + 3$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $2 x^{2}$ from $- x^{2}$ .

$- 3 x^{2} + 1 + 2 x - 10 + 3$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Subtract $10$ from $1$ .

$- 3 x^{2} + 2 x - 9 + 3$

Step 2.2.2

Add $- 9$ and $3$ .

$- 3 x^{2} + 2 x - 6$