Basic Math Examples

$(3 x - 7) (2 x + 9)$

Step 1

Expand $(3 x - 7) (2 x + 9)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 x (2 x + 9) - 7 (2 x + 9)$

Step 1.2

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 9 - 7 (2 x + 9)$

Step 1.3

Apply the distributive property.

$3 x (2 x) + 3 x \cdot 9 - 7 (2 x) - 7 \cdot 9$

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

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x \cdot x + 3 x \cdot 9 - 7 (2 x) - 7 \cdot 9$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$3 \cdot 2 (x \cdot x) + 3 x \cdot 9 - 7 (2 x) - 7 \cdot 9$

Step 2.1.2.2

Multiply $x$ by $x$ .

$3 \cdot 2 x^{2} + 3 x \cdot 9 - 7 (2 x) - 7 \cdot 9$

Step 2.1.3

Multiply $3$ by $2$ .

$6 x^{2} + 3 x \cdot 9 - 7 (2 x) - 7 \cdot 9$

Step 2.1.4

Multiply $9$ by $3$ .

$6 x^{2} + 27 x - 7 (2 x) - 7 \cdot 9$

Step 2.1.5

Multiply $2$ by $- 7$ .

$6 x^{2} + 27 x - 14 x - 7 \cdot 9$

Step 2.1.6

Multiply $- 7$ by $9$ .

$6 x^{2} + 27 x - 14 x - 63$

Step 2.2

Subtract $14 x$ from $27 x$ .

$6 x^{2} + 13 x - 63$