Algebra Examples

$a x^{2} - (1 + a b) x y + b y^{2}$

Step 1

Apply the distributive property.

$a x^{2} + (- 1 \cdot 1 - (a b)) x y + b y^{2}$

Step 2

Multiply $- 1$ by $1$ .

$a x^{2} + (- 1 - (a b)) x y + b y^{2}$

Step 3

Remove parentheses.

$a x^{2} + (- 1 - a b) x y + b y^{2}$

Step 4

Apply the distributive property.

$a x^{2} + (- 1 x - a b x) y + b y^{2}$

Step 5

Rewrite $- 1 x$ as $- x$ .

$a x^{2} + (- x - a b x) y + b y^{2}$

Step 6

Apply the distributive property.

$a x^{2} - x y - a b x y + b y^{2}$

Step 7

Rewrite $a x^{2} - x y - a b x y + b y^{2}$ in a factored form.

Tap for more steps...

Step 7.1

Factor out the greatest common factor from each group.

Tap for more steps...

Step 7.1.1

Group the first two terms and the last two terms.

$(a x^{2} - x y) - a b x y + b y^{2}$

Step 7.1.2

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

$x (a x - 1 y) - b y (a x - 1 y)$

Step 7.2

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

$(a x - 1 y) (x - b y)$

Step 7.3

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

$(a x - y) (x - b y)$