Basic Math Examples

$2 y - 1 \sqrt{6 y^{2} + 13 y - 8}$

Step 1

Factor by grouping.

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Step 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 $a \cdot c = 6 \cdot - 8 = - 48$ and whose sum is $b = 13$ .

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Step 1.1.1

Factor $13$ out of $13 y$ .

$2 y - 1 \sqrt{6 y^{2} + 13 (y) - 8}$

Step 1.1.2

Rewrite $13$ as $- 3$ plus $16$

$2 y - 1 \sqrt{6 y^{2} + (- 3 + 16) y - 8}$

Step 1.1.3

Apply the distributive property.

$2 y - 1 \sqrt{6 y^{2} - 3 y + 16 y - 8}$

Step 1.2

Factor out the greatest common factor from each group.

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Step 1.2.1

Group the first two terms and the last two terms.

$2 y - 1 \sqrt{(6 y^{2} - 3 y) + 16 y - 8}$

Step 1.2.2

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

$2 y - 1 \sqrt{3 y (2 y - 1) + 8 (2 y - 1)}$

Step 1.3

Factor the polynomial by factoring out the greatest common factor, $2 y - 1$ .

$2 y - 1 \sqrt{(2 y - 1) (3 y + 8)}$

Step 2

Rewrite $- 1 \sqrt{(2 y - 1) (3 y + 8)}$ as $- \sqrt{(2 y - 1) (3 y + 8)}$ .

$2 y - \sqrt{(2 y - 1) (3 y + 8)}$