Algebra Examples

$(b + 2) (b - 4) = 0$

Step 1

Simplify $(b + 2) (b - 4)$ .

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Step 1.1

Expand $(b + 2) (b - 4)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$b (b - 4) + 2 (b - 4) = 0$

Step 1.1.2

Apply the distributive property.

$b \cdot b + b \cdot - 4 + 2 (b - 4) = 0$

Step 1.1.3

Apply the distributive property.

$b \cdot b + b \cdot - 4 + 2 b + 2 \cdot - 4 = 0$

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 $b$ by $b$ .

$b^{2} + b \cdot - 4 + 2 b + 2 \cdot - 4 = 0$

Step 1.2.1.2

Move $- 4$ to the left of $b$ .

$b^{2} - 4 \cdot b + 2 b + 2 \cdot - 4 = 0$

Step 1.2.1.3

Multiply $2$ by $- 4$ .

$b^{2} - 4 b + 2 b - 8 = 0$

Step 1.2.2

Add $- 4 b$ and $2 b$ .

$b^{2} - 2 b - 8 = 0$

Step 2

Factor $b^{2} - 2 b - 8$ using the AC method.

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Step 2.1

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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Step 2.2

Write the factored form using these integers.

$(b - 4) (b + 2) = 0$

Step 3

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

$b - 4 = 0$

$b + 2 = 0$

Step 4

Set $b - 4$ equal to $0$ and solve for $b$ .

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Step 4.1

Set $b - 4$ equal to $0$ .

$b - 4 = 0$

Step 4.2

Add $4$ to both sides of the equation.

$b = 4$

Step 5

Set $b + 2$ equal to $0$ and solve for $b$ .

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Step 5.1

Set $b + 2$ equal to $0$ .

$b + 2 = 0$

Step 5.2

Subtract $2$ from both sides of the equation.

$b = - 2$

Step 6

The final solution is all the values that make $(b - 4) (b + 2) = 0$ true.

$b = 4, - 2$

Step 7