Algebra Examples

$3 x (x - 3 y) + 9 y (3 y - x)$

Step 1

Factor $3$ out of $3 x (x - 3 y) + 9 y (3 y - x)$ .

Tap for more steps...

Step 1.1

Factor $3$ out of $3 x (x - 3 y)$ .

$3 (x (x - 3 y)) + 9 y (3 y - x)$

Step 1.2

Factor $3$ out of $9 y (3 y - x)$ .

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

Step 1.3

Factor $3$ out of $3 (x (x - 3 y)) + 3 (3 y (3 y - x))$ .

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $x$ by $x$ .

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

Step 4

Rewrite using the commutative property of multiplication.

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

Step 5

Apply the distributive property.

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

Step 6

Rewrite using the commutative property of multiplication.

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

Step 7

Rewrite using the commutative property of multiplication.

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

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

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

Tap for more steps...

Step 8.1.1

Move $y$ .

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

Step 8.1.2

Multiply $y$ by $y$ .

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

Step 8.2

Multiply $3$ by $3$ .

$3 (x^{2} - 3 x y + 9 y^{2} + 3 \cdot - 1 y x)$

Step 8.3

Multiply $3$ by $- 1$ .

$3 (x^{2} - 3 x y + 9 y^{2} - 3 y x)$

Step 9

Subtract $3 y x$ from $- 3 x y$ .

Tap for more steps...

Step 9.1

Move $y$ .

$3 (x^{2} + 9 y^{2} - 3 x y - 3 x y)$

Step 9.2

Subtract $3 x y$ from $- 3 x y$ .

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

Step 10

Factor using the perfect square rule.

Tap for more steps...

Step 10.1

Rearrange terms.

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

Step 10.2

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

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

Step 10.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 x y = 2 \cdot x \cdot (3 y)$

Step 10.4

Rewrite the polynomial.

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

Step 10.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3 y$ .

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