Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

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

Step 2.1.2

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

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

Step 2.1.3

Multiply $x$ by $1$ .

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

Step 2.1.4

Multiply $2$ by $1$ .

$(x^{2} + 2 x + x + 2) (y - 3)$

Step 2.2

Add $2 x$ and $x$ .

$(x^{2} + 3 x + 2) (y - 3)$

Step 3

Expand $(x^{2} + 3 x + 2) (y - 3)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} y + x^{2} \cdot - 3 + 3 x y + 3 x \cdot - 3 + 2 y + 2 \cdot - 3$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Move $- 3$ to the left of $x^{2}$ .

$x^{2} y - 3 \cdot x^{2} + 3 x y + 3 x \cdot - 3 + 2 y + 2 \cdot - 3$

Step 4.1.2

Multiply $- 3$ by $3$ .

$x^{2} y - 3 x^{2} + 3 x y - 9 x + 2 y + 2 \cdot - 3$

Step 4.1.3

Multiply $2$ by $- 3$ .

$x^{2} y - 3 x^{2} + 3 x y - 9 x + 2 y - 6$

Step 4.2

Reorder.

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Step 4.2.1

Move $- 9 x$ .

$x^{2} y - 3 x^{2} + 3 x y + 2 y - 9 x - 6$

Step 4.2.2

Move $- 3 x^{2}$ .

$x^{2} y + 3 x y - 3 x^{2} + 2 y - 9 x - 6$