Algebra Examples

$x (y - 3) + n (3 - y)$

Step 1

Apply the distributive property.

$x y + x \cdot - 3 + n (3 - y)$

Step 2

Move $- 3$ to the left of $x$ .

$x y - 3 x + n (3 - y)$

Step 3

Apply the distributive property.

$x y - 3 x + n \cdot 3 + n (- y)$

Step 4

Move $3$ to the left of $n$ .

$x y - 3 x + 3 \cdot n + n (- y)$

Step 5

Rewrite using the commutative property of multiplication.

$x y - 3 x + 3 n - n y$

Step 6

Rewrite $x y - 3 x + 3 n - n y$ in a factored form.

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Step 6.1

Regroup terms.

$- 3 x + x y + 3 n - n y$

Step 6.2

Factor out the greatest common factor from each group.

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Step 6.2.1

Group the first two terms and the last two terms.

$(- 3 x + x y) + 3 n - n y$

Step 6.2.2

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

$x \cdot (- 3 + y) - n (- 3 + y)$

Step 6.3

Factor the polynomial by factoring out the greatest common factor, $- 3 + y$ .

$(- 3 + y) (x - n)$