Algebra Examples

$3 x (4 x - 9 y) (4 x + 9 y)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$(3 x (4 x) + 3 x (- 9 y)) (4 x + 9 y)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$(3 \cdot 4 x \cdot x + 3 x (- 9 y)) (4 x + 9 y)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$(3 \cdot 4 x \cdot x + 3 \cdot - 9 x y) (4 x + 9 y)$

Step 1.3

Simplify each term.

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Step 1.3.1

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

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Step 1.3.1.1

Move $x$ .

$(3 \cdot 4 (x \cdot x) + 3 \cdot - 9 x y) (4 x + 9 y)$

Step 1.3.1.2

Multiply $x$ by $x$ .

$(3 \cdot 4 x^{2} + 3 \cdot - 9 x y) (4 x + 9 y)$

Step 1.3.2

Multiply $3$ by $4$ .

$(12 x^{2} + 3 \cdot - 9 x y) (4 x + 9 y)$

Step 1.3.3

Multiply $3$ by $- 9$ .

$(12 x^{2} - 27 x y) (4 x + 9 y)$

Step 2

Expand $(12 x^{2} - 27 x y) (4 x + 9 y)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$12 x^{2} (4 x + 9 y) - 27 x y (4 x + 9 y)$

Step 2.2

Apply the distributive property.

$12 x^{2} (4 x) + 12 x^{2} (9 y) - 27 x y (4 x + 9 y)$

Step 2.3

Apply the distributive property.

$12 x^{2} (4 x) + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$12 \cdot 4 x^{2} x + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.2

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 3.1.2.1

Move $x$ .

$12 \cdot 4 (x \cdot x^{2}) + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.2.2

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

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Step 3.1.2.2.1

Raise $x$ to the power of $1$ .

$12 \cdot 4 (x^{1} x^{2}) + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 \cdot 4 x^{1 + 2} + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.2.3

Add $1$ and $2$ .

$12 \cdot 4 x^{3} + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.3

Multiply $12$ by $4$ .

$48 x^{3} + 12 x^{2} (9 y) - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$48 x^{3} + 12 \cdot 9 x^{2} y - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.5

Multiply $12$ by $9$ .

$48 x^{3} + 108 x^{2} y - 27 x y (4 x) - 27 x y (9 y)$

Step 3.1.6

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

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Step 3.1.6.1

Move $x$ .

$48 x^{3} + 108 x^{2} y - 27 (x \cdot x) y \cdot 4 - 27 x y (9 y)$

Step 3.1.6.2

Multiply $x$ by $x$ .

$48 x^{3} + 108 x^{2} y - 27 x^{2} y \cdot 4 - 27 x y (9 y)$

Step 3.1.7

Multiply $4$ by $- 27$ .

$48 x^{3} + 108 x^{2} y - 108 x^{2} y - 27 x y (9 y)$

Step 3.1.8

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

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Step 3.1.8.1

Move $y$ .

$48 x^{3} + 108 x^{2} y - 108 x^{2} y - 27 x (y \cdot y) \cdot 9$

Step 3.1.8.2

Multiply $y$ by $y$ .

$48 x^{3} + 108 x^{2} y - 108 x^{2} y - 27 x y^{2} \cdot 9$

Step 3.1.9

Multiply $9$ by $- 27$ .

$48 x^{3} + 108 x^{2} y - 108 x^{2} y - 243 x y^{2}$

Step 3.2

Subtract $108 x^{2} y$ from $108 x^{2} y$ .

$48 x^{3} + 0 - 243 x y^{2}$

Step 3.3

Add $48 x^{3}$ and $0$ .

$48 x^{3} - 243 x y^{2}$