Algebra Examples

$x (x - 2) + 2 - x$

Step 1

Apply the distributive property.

$x \cdot x + x \cdot - 2 + 2 - x$

Step 2

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 + 2 - x$

Step 3

Move $- 2$ to the left of $x$ .

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

Step 4

Subtract $x$ from $- 2 x$ .

$x^{2} - 3 x + 2$

Step 5

Factor $x^{2} - 3 x + 2$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $- 3$ .

$- 2, - 1$

Step 5.2

Write the factored form using these integers.

$(x - 2) (x - 1)$