Pre-Algebra Examples

$(x + 7) (x - 1) + (x + 7) (x - 2)$

Step 1

Simplify each term.

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Step 1.1

Expand $(x + 7) (x - 1)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$x (x - 1) + 7 (x - 1) + (x + 7) (x - 2)$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 7 (x - 1) + (x + 7) (x - 2)$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 7 x + 7 \cdot - 1 + (x + 7) (x - 2)$

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 $x$ by $x$ .

$x^{2} + x \cdot - 1 + 7 x + 7 \cdot - 1 + (x + 7) (x - 2)$

Step 1.2.1.2

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x + 7 x + 7 \cdot - 1 + (x + 7) (x - 2)$

Step 1.2.1.3

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x + 7 x + 7 \cdot - 1 + (x + 7) (x - 2)$

Step 1.2.1.4

Multiply $7$ by $- 1$ .

$x^{2} - x + 7 x - 7 + (x + 7) (x - 2)$

Step 1.2.2

Add $- x$ and $7 x$ .

$x^{2} + 6 x - 7 + (x + 7) (x - 2)$

Step 1.3

Expand $(x + 7) (x - 2)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$x^{2} + 6 x - 7 + x (x - 2) + 7 (x - 2)$

Step 1.3.2

Apply the distributive property.

$x^{2} + 6 x - 7 + x \cdot x + x \cdot - 2 + 7 (x - 2)$

Step 1.3.3

Apply the distributive property.

$x^{2} + 6 x - 7 + x \cdot x + x \cdot - 2 + 7 x + 7 \cdot - 2$

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 $x$ by $x$ .

$x^{2} + 6 x - 7 + x^{2} + x \cdot - 2 + 7 x + 7 \cdot - 2$

Step 1.4.1.2

Move $- 2$ to the left of $x$ .

$x^{2} + 6 x - 7 + x^{2} - 2 \cdot x + 7 x + 7 \cdot - 2$

Step 1.4.1.3

Multiply $7$ by $- 2$ .

$x^{2} + 6 x - 7 + x^{2} - 2 x + 7 x - 14$

Step 1.4.2

Add $- 2 x$ and $7 x$ .

$x^{2} + 6 x - 7 + x^{2} + 5 x - 14$

Step 2

Simplify by adding terms.

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Step 2.1

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} + 6 x - 7 + 5 x - 14$

Step 2.2

Add $6 x$ and $5 x$ .

$2 x^{2} + 11 x - 7 - 14$

Step 2.3

Subtract $14$ from $- 7$ .

$2 x^{2} + 11 x - 21$

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 $a \cdot c = 2 \cdot - 21 = - 42$ and whose sum is $b = 11$ .

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Step 3.1.1

Factor $11$ out of $11 x$ .

$2 x^{2} + 11 (x) - 21$

Step 3.1.2

Rewrite $11$ as $- 3$ plus $14$

$2 x^{2} + (- 3 + 14) x - 21$

Step 3.1.3

Apply the distributive property.

$2 x^{2} - 3 x + 14 x - 21$

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.

$(2 x^{2} - 3 x) + 14 x - 21$

Step 3.2.2

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

$x (2 x - 3) + 7 (2 x - 3)$

Step 3.3

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (x + 7)$