Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

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

Step 2.2

Multiply $x$ by $x$ .

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $5$ by $- 1$ .

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

Step 5

Apply the distributive property.

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

Step 6

Multiply $- - x$ .

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Step 6.1

Multiply $- 1$ by $- 1$ .

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

Step 6.2

Multiply $x$ by $1$ .

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

Step 7

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

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

Step 7.1.2

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

$5 x (x - y) + 1 (x - y)$

Step 7.2

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

$(x - y) (5 x + 1)$