Algebra Examples

$25 x^{2} - {(x + 2 y + 4 z)}^{2}$

Step 1

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

${(5 x)}^{2} - {(x + 2 y + 4 z)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x$ and $b = x + 2 y + 4 z$ .

$(5 x + x + 2 y + 4 z) (5 x - (x + 2 y + 4 z))$

Step 3

Simplify.

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Step 3.1

Add $5 x$ and $x$ .

$(6 x + 2 y + 4 z) (5 x - (x + 2 y + 4 z))$

Step 3.2

Factor $2$ out of $6 x + 2 y + 4 z$ .

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Step 3.2.1

Factor $2$ out of $6 x$ .

$(2 (3 x) + 2 y + 4 z) (5 x - (x + 2 y + 4 z))$

Step 3.2.2

Factor $2$ out of $2 y$ .

$(2 (3 x) + 2 (y) + 4 z) (5 x - (x + 2 y + 4 z))$

Step 3.2.3

Factor $2$ out of $4 z$ .

$(2 (3 x) + 2 (y) + 2 (2 z)) (5 x - (x + 2 y + 4 z))$

Step 3.2.4

Factor $2$ out of $2 (3 x) + 2 (y)$ .

$(2 (3 x + y) + 2 (2 z)) (5 x - (x + 2 y + 4 z))$

Step 3.2.5

Factor $2$ out of $2 (3 x + y) + 2 (2 z)$ .

$2 (3 x + y + 2 z) (5 x - (x + 2 y + 4 z))$

Step 3.3

Apply the distributive property.

$2 (3 x + y + 2 z) (5 x - x - (2 y) - (4 z))$

Step 3.4

Simplify.

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Step 3.4.1

Multiply $2$ by $- 1$ .

$2 (3 x + y + 2 z) (5 x - x - 2 y - (4 z))$

Step 3.4.2

Multiply $4$ by $- 1$ .

$2 (3 x + y + 2 z) (5 x - x - 2 y - 4 z)$

Step 3.5

Subtract $x$ from $5 x$ .

$2 (3 x + y + 2 z) (4 x - 2 y - 4 z)$

Step 3.6

Factor.

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Step 3.6.1

Factor $2$ out of $4 x - 2 y - 4 z$ .

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Step 3.6.1.1

Factor $2$ out of $4 x$ .

$2 (3 x + y + 2 z) (2 (2 x) - 2 y - 4 z)$

Step 3.6.1.2

Factor $2$ out of $- 2 y$ .

$2 (3 x + y + 2 z) (2 (2 x) + 2 (- y) - 4 z)$

Step 3.6.1.3

Factor $2$ out of $- 4 z$ .

$2 (3 x + y + 2 z) (2 (2 x) + 2 (- y) + 2 (- 2 z))$

Step 3.6.1.4

Factor $2$ out of $2 (2 x) + 2 (- y)$ .

$2 (3 x + y + 2 z) (2 (2 x - y) + 2 (- 2 z))$

Step 3.6.1.5

Factor $2$ out of $2 (2 x - y) + 2 (- 2 z)$ .

$2 (3 x + y + 2 z) (2 (2 x - y - 2 z))$

Step 3.6.2

Remove unnecessary parentheses.

$2 (3 x + y + 2 z) \cdot 2 (2 x - y - 2 z)$

Step 3.7

Multiply $2$ by $2$ .

$4 (3 x + y + 2 z) (2 x - y - 2 z)$