Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Multiply $y$ by $y$ by adding the exponents.

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Step 1.3.1

Move $y$ .

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

Step 1.3.2

Multiply $y$ by $y$ .

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

Step 1.4

Multiply $- 1$ by $3$ .

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x - 3 y x - y^{2} + y^{2}$ .

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Step 2.1.1

Add $- y^{2}$ and $y^{2}$ .

$3 (x - 3 y x + 0)$

Step 2.1.2

Add $x - 3 y x$ and $0$ .

$3 (x - 3 y x)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Multiply $- 3$ by $3$ .

$3 x - 9 y x$