Basic Math Examples

$(v - 1) (v + 5) = v^{2} + 4 v - 2$

Step 1

Simplify $(v - 1) (v + 5)$ .

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Step 1.1

Rewrite.

$0 + 0 + (v - 1) (v + 5) = v^{2} + 4 v - 2$

Step 1.2

Simplify by adding zeros.

$(v - 1) (v + 5) = v^{2} + 4 v - 2$

Step 1.3

Expand $(v - 1) (v + 5)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$v (v + 5) - 1 (v + 5) = v^{2} + 4 v - 2$

Step 1.3.2

Apply the distributive property.

$v \cdot v + v \cdot 5 - 1 (v + 5) = v^{2} + 4 v - 2$

Step 1.3.3

Apply the distributive property.

$v \cdot v + v \cdot 5 - 1 v - 1 \cdot 5 = v^{2} + 4 v - 2$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $v$ by $v$ .

$v^{2} + v \cdot 5 - 1 v - 1 \cdot 5 = v^{2} + 4 v - 2$

Step 1.4.1.2

Move $5$ to the left of $v$ .

$v^{2} + 5 \cdot v - 1 v - 1 \cdot 5 = v^{2} + 4 v - 2$

Step 1.4.1.3

Rewrite $- 1 v$ as $- v$ .

$v^{2} + 5 v - v - 1 \cdot 5 = v^{2} + 4 v - 2$

Step 1.4.1.4

Multiply $- 1$ by $5$ .

$v^{2} + 5 v - v - 5 = v^{2} + 4 v - 2$

Step 1.4.2

Subtract $v$ from $5 v$ .

$v^{2} + 4 v - 5 = v^{2} + 4 v - 2$

Step 2

Move all terms containing $v$ to the left side of the equation.

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Step 2.1

Subtract $v^{2}$ from both sides of the equation.

$v^{2} + 4 v - 5 - v^{2} = 4 v - 2$

Step 2.2

Subtract $4 v$ from both sides of the equation.

$v^{2} + 4 v - 5 - v^{2} - 4 v = - 2$

Step 2.3

Combine the opposite terms in $v^{2} + 4 v - 5 - v^{2} - 4 v$ .

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Step 2.3.1

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

$4 v - 5 + 0 - 4 v = - 2$

Step 2.3.2

Add $4 v - 5$ and $0$ .

$4 v - 5 - 4 v = - 2$

Step 2.3.3

Subtract $4 v$ from $4 v$ .

$0 - 5 = - 2$

Step 2.3.4

Subtract $5$ from $0$ .

$- 5 = - 2$

Step 3

Since $- 5 \neq - 2$ , there are no solutions.

No solution