Algebra Examples

$(x - r) (x - s)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Expand $(x - r) (x - s)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x - s) - r (x - s)$

Step 2.2

Apply the distributive property.

$x \cdot x + x (- s) - r (x - s)$

Step 2.3

Apply the distributive property.

$x \cdot x + x (- s) - r x - r (- s)$

Step 3

Simplify terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$x^{2} + x (- s) - r x - r (- s)$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$x^{2} - x s - r x - r (- s)$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$x^{2} - x s - r x - 1 \cdot - 1 r s$

Step 3.1.4

Multiply $- 1$ by $- 1$ .

$x^{2} - x s - r x + 1 r s$

Step 3.1.5

Multiply $r$ by $1$ .

$x^{2} - x s - r x + r s$

Step 3.2

Simplify the expression.

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Step 3.2.1

Move $x$ .

$x^{2} - s x - r x + r s$

Step 3.2.2

Move $x^{2}$ .

$- s x - r x + r s + x^{2}$

Step 3.2.3

Move $- s x$ .

$- r x + r s - s x + x^{2}$

Step 3.2.4

Reorder $- r x$ and $r s$ .

$r s - r x - s x + x^{2}$