Algebra Examples

$16 x^{2} - y^{2} - 2 y z - z^{2}$

Step 1

Regroup terms.

$16 x^{2} - y^{2} - 2 y z - z^{2}$

Step 2

Factor $- 1$ out of $- y^{2} - 2 y z - z^{2}$ .

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Step 2.1

Factor $- 1$ out of $- y^{2}$ .

$16 x^{2} - (y^{2}) - 2 y z - z^{2}$

Step 2.2

Factor $- 1$ out of $- 2 y z$ .

$16 x^{2} - (y^{2}) - (2 y z) - z^{2}$

Step 2.3

Factor $- 1$ out of $- z^{2}$ .

$16 x^{2} - (y^{2}) - (2 y z) - (z^{2})$

Step 2.4

Factor $- 1$ out of $- (y^{2}) - (2 y z)$ .

$16 x^{2} - (y^{2} + 2 y z) - (z^{2})$

Step 2.5

Factor $- 1$ out of $- (y^{2} + 2 y z) - (z^{2})$ .

$16 x^{2} - (y^{2} + 2 y z + z^{2})$

Step 3

Factor using the perfect square rule.

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Step 3.1

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 y z = 2 \cdot y \cdot z$

Step 3.2

Rewrite the polynomial.

$16 x^{2} - (y^{2} + 2 \cdot y \cdot z + z^{2})$

Step 3.3

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = z$ .

$16 x^{2} - {(y + z)}^{2}$

Step 4

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

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

Step 5

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

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

Step 6

Apply the distributive property.

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