Pre-Algebra Examples

$(x - 3) (x - 2) - (x - 2) (1 - x) + (1 - x)$

Step 1

Remove parentheses.

$(x - 3) (x - 2) - (x - 2) (1 - x) + 1 - x$

Step 2

Simplify each term.

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Step 2.1

Expand $(x - 3) (x - 2)$ using the FOIL Method.

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Step 2.1.1

Apply the distributive property.

$x (x - 2) - 3 (x - 2) - (x - 2) (1 - x) + 1 - x$

Step 2.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 3 (x - 2) - (x - 2) (1 - x) + 1 - x$

Step 2.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 2 - 3 x - 3 \cdot - 2 - (x - 2) (1 - x) + 1 - x$

Step 2.2

Simplify and combine like terms.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2 - 3 x - 3 \cdot - 2 - (x - 2) (1 - x) + 1 - x$

Step 2.2.1.2

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

$x^{2} - 2 \cdot x - 3 x - 3 \cdot - 2 - (x - 2) (1 - x) + 1 - x$

Step 2.2.1.3

Multiply $- 3$ by $- 2$ .

$x^{2} - 2 x - 3 x + 6 - (x - 2) (1 - x) + 1 - x$

Step 2.2.2

Subtract $3 x$ from $- 2 x$ .

$x^{2} - 5 x + 6 - (x - 2) (1 - x) + 1 - x$

Step 2.3

Apply the distributive property.

$x^{2} - 5 x + 6 + (- x - - 2) (1 - x) + 1 - x$

Step 2.4

Multiply $- 1$ by $- 2$ .

$x^{2} - 5 x + 6 + (- x + 2) (1 - x) + 1 - x$

Step 2.5

Expand $(- x + 2) (1 - x)$ using the FOIL Method.

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Step 2.5.1

Apply the distributive property.

$x^{2} - 5 x + 6 - x (1 - x) + 2 (1 - x) + 1 - x$

Step 2.5.2

Apply the distributive property.

$x^{2} - 5 x + 6 - x \cdot 1 - x (- x) + 2 (1 - x) + 1 - x$

Step 2.5.3

Apply the distributive property.

$x^{2} - 5 x + 6 - x \cdot 1 - x (- x) + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6

Simplify and combine like terms.

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Step 2.6.1

Simplify each term.

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Step 2.6.1.1

Multiply $- 1$ by $1$ .

$x^{2} - 5 x + 6 - x - x (- x) + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6.1.2

Rewrite using the commutative property of multiplication.

$x^{2} - 5 x + 6 - x - 1 \cdot - 1 x \cdot x + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6.1.3

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

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Step 2.6.1.3.1

Move $x$ .

$x^{2} - 5 x + 6 - x - 1 \cdot - 1 (x \cdot x) + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6.1.3.2

Multiply $x$ by $x$ .

$x^{2} - 5 x + 6 - x - 1 \cdot - 1 x^{2} + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6.1.4

Multiply $- 1$ by $- 1$ .

$x^{2} - 5 x + 6 - x + 1 x^{2} + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6.1.5

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

$x^{2} - 5 x + 6 - x + x^{2} + 2 \cdot 1 + 2 (- x) + 1 - x$

Step 2.6.1.6

Multiply $2$ by $1$ .

$x^{2} - 5 x + 6 - x + x^{2} + 2 + 2 (- x) + 1 - x$

Step 2.6.1.7

Multiply $- 1$ by $2$ .

$x^{2} - 5 x + 6 - x + x^{2} + 2 - 2 x + 1 - x$

Step 2.6.2

Subtract $2 x$ from $- x$ .

$x^{2} - 5 x + 6 - 3 x + x^{2} + 2 + 1 - x$

Step 3

Simplify by adding terms.

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Step 3.1

Add $x^{2}$ and $x^{2}$ .

$2 x^{2} - 5 x + 6 - 3 x + 2 + 1 - x$

Step 3.2

Subtract $3 x$ from $- 5 x$ .

$2 x^{2} - 8 x + 6 + 2 + 1 - x$

Step 3.3

Subtract $x$ from $- 8 x$ .

$2 x^{2} - 9 x + 6 + 2 + 1$

Step 3.4

Simplify by adding numbers.

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Step 3.4.1

Add $6$ and $2$ .

$2 x^{2} - 9 x + 8 + 1$

Step 3.4.2

Add $8$ and $1$ .

$2 x^{2} - 9 x + 9$