Algebra Examples

$3 x^{3} - n x^{2} + 12 x y^{2} + 3 x z - n z - 4 n y^{2}$

Step 1

Regroup terms.

$3 x^{3} - n x^{2} + 12 x y^{2} + 3 x z - n z - 4 n y^{2}$

Step 2

Factor $x^{2}$ out of $3 x^{3} - n x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $3 x^{3}$ .

$x^{2} (3 x) - n x^{2} + 12 x y^{2} + 3 x z - n z - 4 n y^{2}$

Step 2.2

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

$x^{2} (3 x) + x^{2} (- n) + 12 x y^{2} + 3 x z - n z - 4 n y^{2}$

Step 2.3

Factor $x^{2}$ out of $x^{2} (3 x) + x^{2} (- n)$ .

$x^{2} (3 x - n) + 12 x y^{2} + 3 x z - n z - 4 n y^{2}$

Step 3

Regroup terms.

$x^{2} (3 x - n) + 12 x y^{2} - 4 n y^{2} + 3 x z - n z$

Step 4

Factor $4 y^{2}$ out of $12 x y^{2} - 4 n y^{2}$ .

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Step 4.1

Factor $4 y^{2}$ out of $12 x y^{2}$ .

$x^{2} (3 x - n) + 4 y^{2} (3 x) - 4 n y^{2} + 3 x z - n z$

Step 4.2

Factor $4 y^{2}$ out of $- 4 n y^{2}$ .

$x^{2} (3 x - n) + 4 y^{2} (3 x) + 4 y^{2} (- n) + 3 x z - n z$

Step 4.3

Factor $4 y^{2}$ out of $4 y^{2} (3 x) + 4 y^{2} (- n)$ .

$x^{2} (3 x - n) + 4 y^{2} (3 x - n) + 3 x z - n z$

Step 5

Factor $z$ out of $3 x z - n z$ .

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Step 5.1

Factor $z$ out of $3 x z$ .

$x^{2} (3 x - n) + 4 y^{2} (3 x - n) + z (3 x) - n z$

Step 5.2

Factor $z$ out of $- n z$ .

$x^{2} (3 x - n) + 4 y^{2} (3 x - n) + z (3 x) + z (- n)$

Step 5.3

Factor $z$ out of $z (3 x) + z (- n)$ .

$x^{2} (3 x - n) + 4 y^{2} (3 x - n) + z (3 x - n)$

Step 6

Factor $3 x - n$ out of $4 y^{2} (3 x - n) + z (3 x - n)$ .

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Step 6.1

Factor $3 x - n$ out of $4 y^{2} (3 x - n)$ .

$x^{2} (3 x - n) + (3 x - n) (4 y^{2}) + z (3 x - n)$

Step 6.2

Factor $3 x - n$ out of $z (3 x - n)$ .

$x^{2} (3 x - n) + (3 x - n) (4 y^{2}) + (3 x - n) z$

Step 6.3

Factor $3 x - n$ out of $(3 x - n) (4 y^{2}) + (3 x - n) z$ .

$x^{2} (3 x - n) + (3 x - n) (4 y^{2} + z)$

Step 7

Factor $3 x - n$ out of $x^{2} (3 x - n) + (3 x - n) (4 y^{2} + z)$ .

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Step 7.1

Factor $3 x - n$ out of $x^{2} (3 x - n)$ .

$(3 x - n) x^{2} + (3 x - n) (4 y^{2} + z)$

Step 7.2

Factor $3 x - n$ out of $(3 x - n) x^{2} + (3 x - n) (4 y^{2} + z)$ .

$(3 x - n) (x^{2} + 4 y^{2} + z)$