Pre-Algebra Examples

$(5 x - 22) (x + 40)$

Step 1

Expand $(5 x - 22) (x + 40)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 x (x + 40) - 22 (x + 40)$

Step 1.2

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 40 - 22 (x + 40)$

Step 1.3

Apply the distributive property.

$5 x \cdot x + 5 x \cdot 40 - 22 x - 22 \cdot 40$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x$ .

$5 (x \cdot x) + 5 x \cdot 40 - 22 x - 22 \cdot 40$

Step 2.1.1.2

Multiply $x$ by $x$ .

$5 x^{2} + 5 x \cdot 40 - 22 x - 22 \cdot 40$

Step 2.1.2

Multiply $40$ by $5$ .

$5 x^{2} + 200 x - 22 x - 22 \cdot 40$

Step 2.1.3

Multiply $- 22$ by $40$ .

$5 x^{2} + 200 x - 22 x - 880$

Step 2.2

Subtract $22 x$ from $200 x$ .

$5 x^{2} + 178 x - 880$

Step 3

Factor by grouping.

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Step 3.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 5 \cdot - 880 = - 4400$ and whose sum is $b = 178$ .

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Step 3.1.1

Factor $178$ out of $178 x$ .

$5 x^{2} + 178 (x) - 880$

Step 3.1.2

Rewrite $178$ as $- 22$ plus $200$

$5 x^{2} + (- 22 + 200) x - 880$

Step 3.1.3

Apply the distributive property.

$5 x^{2} - 22 x + 200 x - 880$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$(5 x^{2} - 22 x) + 200 x - 880$

Step 3.2.2

Factor out the greatest common factor (GCF) from each group.

$x (5 x - 22) + 40 (5 x - 22)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $5 x - 22$ .

$(5 x - 22) (x + 40)$