Basic Math Examples

$15 k^{2} + 14 k h^{2} - 8 h^{4}$

Step 1

Factor $- 1$ out of $15 k^{2} + 14 k h^{2} - 8 h^{4}$ .

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Step 1.1

Reorder the expression.

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Step 1.1.1

Move $k$ .

$15 k^{2} + 14 h^{2} k - 8 h^{4}$

Step 1.1.2

Move $15 k^{2}$ .

$14 h^{2} k - 8 h^{4} + 15 k^{2}$

Step 1.1.3

Reorder $14 h^{2} k$ and $- 8 h^{4}$ .

$- 8 h^{4} + 14 h^{2} k + 15 k^{2}$

Step 1.2

Factor $- 1$ out of $- 8 h^{4}$ .

$- (8 h^{4}) + 14 h^{2} k + 15 k^{2}$

Step 1.3

Factor $- 1$ out of $14 h^{2} k$ .

$- (8 h^{4}) - (- 14 h^{2} k) + 15 k^{2}$

Step 1.4

Factor $- 1$ out of $15 k^{2}$ .

$- (8 h^{4}) - (- 14 h^{2} k) - (- 15 k^{2})$

Step 1.5

Factor $- 1$ out of $- (8 h^{4}) - (- 14 h^{2} k)$ .

$- (8 h^{4} - 14 h^{2} k) - (- 15 k^{2})$

Step 1.6

Factor $- 1$ out of $- (8 h^{4} - 14 h^{2} k) - (- 15 k^{2})$ .

$- (8 h^{4} - 14 h^{2} k - 15 k^{2})$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

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 $a \cdot c = 8 \cdot - 15 = - 120$ and whose sum is $b = - 14$ .

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Step 2.1.1.1

Reorder terms.

$- (8 h^{4} - 15 k^{2} - 14 h^{2} k)$

Step 2.1.1.2

Reorder $- 15 k^{2}$ and $- 14 h^{2} k$ .

$- (8 h^{4} - 14 h^{2} k - 15 k^{2})$

Step 2.1.1.3

Factor $- 14$ out of $- 14 h^{2} k$ .

$- (8 h^{4} - 14 (h^{2} k) - 15 k^{2})$

Step 2.1.1.4

Rewrite $- 14$ as $6$ plus $- 20$

$- (8 h^{4} + (6 - 20) (h^{2} k) - 15 k^{2})$

Step 2.1.1.5

Apply the distributive property.

$- (8 h^{4} + 6 (h^{2} k) - 20 (h^{2} k) - 15 k^{2})$

Step 2.1.1.6

Remove unnecessary parentheses.

$- (8 h^{4} + 6 h^{2} k - 20 (h^{2} k) - 15 k^{2})$

Step 2.1.1.7

Remove unnecessary parentheses.

$- (8 h^{4} + 6 h^{2} k - 20 h^{2} k - 15 k^{2})$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$- ((8 h^{4} + 6 h^{2} k) - 20 h^{2} k - 15 k^{2})$

Step 2.1.2.2

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

$- (2 h^{2} (4 h^{2} + 3 k) - 5 k (4 h^{2} + 3 k))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $4 h^{2} + 3 k$ .

$- ((4 h^{2} + 3 k) (2 h^{2} - 5 k))$

Step 2.2

Remove unnecessary parentheses.

$- (4 h^{2} + 3 k) (2 h^{2} - 5 k)$