Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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

Step 1.5

Rewrite using the commutative property of multiplication.

$x a - 3 x + 3 y - y a$

Step 2

Reorder terms.

$a x - a y - 3 x + 3 y$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

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

Step 3.2

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

$a (x - y) - 3 (x - y)$

Step 4

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

$(x - y) (a - 3)$