Algebra Examples

$x (y - 5) - y (5 - y)$

Step 1

Apply the distributive property.

$x y + x \cdot - 5 - y (5 - y)$

Step 2

Move $- 5$ to the left of $x$ .

$x y - 5 x - y (5 - y)$

Step 3

Apply the distributive property.

$x y - 5 x - y \cdot 5 - y (- y)$

Step 4

Multiply $5$ by $- 1$ .

$x y - 5 x - 5 y - y (- y)$

Step 5

Rewrite using the commutative property of multiplication.

$x y - 5 x - 5 y - 1 \cdot - 1 y \cdot y$

Step 6

Simplify each term.

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Step 6.1

Multiply $y$ by $y$ by adding the exponents.

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Step 6.1.1

Move $y$ .

$x y - 5 x - 5 y - 1 \cdot - 1 (y \cdot y)$

Step 6.1.2

Multiply $y$ by $y$ .

$x y - 5 x - 5 y - 1 \cdot - 1 y^{2}$

Step 6.2

Multiply $- 1$ by $- 1$ .

$x y - 5 x - 5 y + 1 y^{2}$

Step 6.3

Multiply $y^{2}$ by $1$ .

$x y - 5 x - 5 y + y^{2}$

Step 7

Rewrite $x y - 5 x - 5 y + y^{2}$ in a factored form.

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Step 7.1

Factor out the greatest common factor from each group.

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Step 7.1.1

Group the first two terms and the last two terms.

$(x y - 5 x) - 5 y + y^{2}$

Step 7.1.2

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

$x (y - 5) + y \cdot (y - 5)$

Step 7.2

Factor the polynomial by factoring out the greatest common factor, $y - 5$ .

$(y - 5) (x + y)$