Basic Math Examples

$(P - 1) (P - 3) = 48$

Step 1

Simplify $(P - 1) (P - 3)$ .

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Step 1.1

Expand $(P - 1) (P - 3)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$P (P - 3) - 1 (P - 3) = 48$

Step 1.1.2

Apply the distributive property.

$P \cdot P + P \cdot - 3 - 1 (P - 3) = 48$

Step 1.1.3

Apply the distributive property.

$P \cdot P + P \cdot - 3 - 1 P - 1 \cdot - 3 = 48$

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 $P$ by $P$ .

$P^{2} + P \cdot - 3 - 1 P - 1 \cdot - 3 = 48$

Step 1.2.1.2

Move $- 3$ to the left of $P$ .

$P^{2} - 3 \cdot P - 1 P - 1 \cdot - 3 = 48$

Step 1.2.1.3

Rewrite $- 1 P$ as $- P$ .

$P^{2} - 3 P - P - 1 \cdot - 3 = 48$

Step 1.2.1.4

Multiply $- 1$ by $- 3$ .

$P^{2} - 3 P - P + 3 = 48$

Step 1.2.2

Subtract $P$ from $- 3 P$ .

$P^{2} - 4 P + 3 = 48$

Step 2

Subtract $48$ from both sides of the equation.

$P^{2} - 4 P + 3 - 48 = 0$

Step 3

Subtract $48$ from $3$ .

$P^{2} - 4 P - 45 = 0$

Step 4

Factor $P^{2} - 4 P - 45$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 45$ and whose sum is $- 4$ .

$- 9, 5$

Step 4.2

Write the factored form using these integers.

$(P - 9) (P + 5) = 0$

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$P - 9 = 0$

$P + 5 = 0$

Step 6

Set $P - 9$ equal to $0$ and solve for $P$ .

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Step 6.1

Set $P - 9$ equal to $0$ .

$P - 9 = 0$

Step 6.2

Add $9$ to both sides of the equation.

$P = 9$

Step 7

Set $P + 5$ equal to $0$ and solve for $P$ .

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Step 7.1

Set $P + 5$ equal to $0$ .

$P + 5 = 0$

Step 7.2

Subtract $5$ from both sides of the equation.

$P = - 5$

Step 8

The final solution is all the values that make $(P - 9) (P + 5) = 0$ true.

$P = 9, - 5$