Pre-Algebra Examples

$x^{2} - 100 + 25$ , ${(x - 5)}^{2}$

Step 1

Regroup terms.

$x^{2} + {(x - 5)}^{2} - 100 + 25$

Step 2

Rewrite ${(x - 5)}^{2}$ as $(x - 5) (x - 5)$ .

$x^{2} + (x - 5) (x - 5) - 100 + 25$

Step 3

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

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Step 3.1

Apply the distributive property.

$x^{2} + x (x - 5) - 5 (x - 5) - 100 + 25$

Step 3.2

Apply the distributive property.

$x^{2} + x \cdot x + x \cdot - 5 - 5 (x - 5) - 100 + 25$

Step 3.3

Apply the distributive property.

$x^{2} + x \cdot x + x \cdot - 5 - 5 x - 5 \cdot - 5 - 100 + 25$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $x$ by $x$ .

$x^{2} + x^{2} + x \cdot - 5 - 5 x - 5 \cdot - 5 - 100 + 25$

Step 4.1.2

Move $- 5$ to the left of $x$ .

$x^{2} + x^{2} - 5 x - 5 x - 5 \cdot - 5 - 100 + 25$

Step 4.1.3

Multiply $- 5$ by $- 5$ .

$x^{2} + x^{2} - 5 x - 5 x + 25 - 100 + 25$

Step 4.2

Subtract $5 x$ from $- 5 x$ .

$x^{2} + x^{2} - 10 x + 25 - 100 + 25$

Step 5

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

$2 x^{2} - 10 x + 25 - 100 + 25$

Step 6

Add $- 100$ and $25$ .

$2 x^{2} - 10 x + 25 - 75$

Step 7

Subtract $75$ from $25$ .

$2 x^{2} - 10 x - 50$

Step 8

Factor $2$ out of $2 x^{2} - 10 x - 50$ .

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Step 8.1

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 10 x - 50$

Step 8.2

Factor $2$ out of $- 10 x$ .

$2 (x^{2}) + 2 (- 5 x) - 50$

Step 8.3

Factor $2$ out of $- 50$ .

$2 x^{2} + 2 (- 5 x) + 2 \cdot - 25$

Step 8.4

Factor $2$ out of $2 x^{2} + 2 (- 5 x)$ .

$2 (x^{2} - 5 x) + 2 \cdot - 25$

Step 8.5

Factor $2$ out of $2 (x^{2} - 5 x) + 2 \cdot - 25$ .

$2 (x^{2} - 5 x - 25)$

Step 9

The greatest common factor $GCF$ is the term in front of the factored expression.

$2$