Finite Math Examples

$x^{2} - 3 x - 4 = (x - a) (x - b)$

Step 1

Subtract $(x - a) (x - b)$ from both sides of the equation.

$x^{2} - 3 x - 4 - (x - a) (x - b) = 0$

Step 2

Simplify $x^{2} - 3 x - 4 - (x - a) (x - b)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$x^{2} - 3 x - 4 + (- x - - a) (x - b) = 0$

Step 2.1.2

Multiply $- - a$ .

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Step 2.1.2.1

Multiply $- 1$ by $- 1$ .

$x^{2} - 3 x - 4 + (- x + 1 a) (x - b) = 0$

Step 2.1.2.2

Multiply $a$ by $1$ .

$x^{2} - 3 x - 4 + (- x + a) (x - b) = 0$

Step 2.1.3

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

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Step 2.1.3.1

Apply the distributive property.

$x^{2} - 3 x - 4 - x (x - b) + a (x - b) = 0$

Step 2.1.3.2

Apply the distributive property.

$x^{2} - 3 x - 4 - x \cdot x - x (- b) + a (x - b) = 0$

Step 2.1.3.3

Apply the distributive property.

$x^{2} - 3 x - 4 - x \cdot x - x (- b) + a x + a (- b) = 0$

Step 2.1.4

Simplify each term.

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Step 2.1.4.1

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

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Step 2.1.4.1.1

Move $x$ .

$x^{2} - 3 x - 4 - (x \cdot x) - x (- b) + a x + a (- b) = 0$

Step 2.1.4.1.2

Multiply $x$ by $x$ .

$x^{2} - 3 x - 4 - x^{2} - x (- b) + a x + a (- b) = 0$

Step 2.1.4.2

Rewrite using the commutative property of multiplication.

$x^{2} - 3 x - 4 - x^{2} - 1 \cdot - 1 x b + a x + a (- b) = 0$

Step 2.1.4.3

Multiply $- 1$ by $- 1$ .

$x^{2} - 3 x - 4 - x^{2} + 1 x b + a x + a (- b) = 0$

Step 2.1.4.4

Multiply $x$ by $1$ .

$x^{2} - 3 x - 4 - x^{2} + x b + a x + a (- b) = 0$

Step 2.1.4.5

Rewrite using the commutative property of multiplication.

$x^{2} - 3 x - 4 - x^{2} + x b + a x - a b = 0$

Step 2.2

Combine the opposite terms in $x^{2} - 3 x - 4 - x^{2} + x b + a x - a b$ .

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Step 2.2.1

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

$- 3 x - 4 + 0 + x b + a x - a b = 0$

Step 2.2.2

Add $- 3 x - 4$ and $0$ .

$- 3 x - 4 + x b + a x - a b = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.