Algebra Examples

$(6 y^{2} + y - 2) {(2 y - 1)}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(6 y^{2} + y - 2) \frac{1}{2 y - 1}$

Step 2

Multiply $6 y^{2} + y - 2$ by $\frac{1}{2 y - 1}$ .

$\frac{6 y^{2} + y - 2}{2 y - 1}$

Step 3

Factor by grouping.

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Step 3.1

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 $a \cdot c = 6 \cdot - 2 = - 12$ and whose sum is $b = 1$ .

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Step 3.1.1

Multiply by $1$ .

$\frac{6 y^{2} + 1 y - 2}{2 y - 1}$

Step 3.1.2

Rewrite $1$ as $- 3$ plus $4$

$\frac{6 y^{2} + (- 3 + 4) y - 2}{2 y - 1}$

Step 3.1.3

Apply the distributive property.

$\frac{6 y^{2} - 3 y + 4 y - 2}{2 y - 1}$

Step 3.2

Factor out the greatest common factor from each group.

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Step 3.2.1

Group the first two terms and the last two terms.

$\frac{(6 y^{2} - 3 y) + 4 y - 2}{2 y - 1}$

Step 3.2.2

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

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

Step 3.3

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

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

Step 4

Cancel the common factor of $2 y - 1$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $3 y + 2$ by $1$ .

$3 y + 2$