Factor 4x^2-8xy+3y^2

$4 x^{2} - 8 x y + 3 y^{2}$

Step 1

Factor by grouping.

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 $a \cdot c = 4 \cdot 3 = 12$ and whose sum is $b = - 8$ .

Reorder terms.

$4 x^{2} + 3 y^{2} - 8 x y$

Reorder $3 y^{2}$ and $- 8 x y$ .

$4 x^{2} - 8 x y + 3 y^{2}$

Factor $- 8$ out of $- 8 x y$ .

$4 x^{2} - 8 (x y) + 3 y^{2}$

Rewrite $- 8$ as $- 2$ plus $- 6$

$4 x^{2} + (- 2 - 6) (x y) + 3 y^{2}$

Apply the distributive property.

$4 x^{2} - 2 (x y) - 6 (x y) + 3 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} - 2 x y - 6 (x y) + 3 y^{2}$

Remove unnecessary parentheses.

$4 x^{2} - 2 x y - 6 x y + 3 y^{2}$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 2 x y) - 6 x y + 3 y^{2}$

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

$2 x (2 x - 1 y) - 3 y (2 x - y)$

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

$(2 x - 1 y) (2 x - 3 y)$

Step 2

Rewrite $- 1 y$ as $- y$ .

$(2 x - y) (2 x - 3 y)$

Factor 4x^2-8xy+3y^2

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