Algebra Examples

$(6 x + 1) (1 - 3 x)$

Step 1

Expand $(6 x + 1) (1 - 3 x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$6 x (1 - 3 x) + 1 (1 - 3 x)$

Step 1.2

Apply the distributive property.

$6 x \cdot 1 + 6 x (- 3 x) + 1 (1 - 3 x)$

Step 1.3

Apply the distributive property.

$6 x \cdot 1 + 6 x (- 3 x) + 1 \cdot 1 + 1 (- 3 x)$

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 $6$ by $1$ .

$6 x + 6 x (- 3 x) + 1 \cdot 1 + 1 (- 3 x)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$6 x + 6 \cdot - 3 x \cdot x + 1 \cdot 1 + 1 (- 3 x)$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$6 x + 6 \cdot - 3 (x \cdot x) + 1 \cdot 1 + 1 (- 3 x)$

Step 2.1.3.2

Multiply $x$ by $x$ .

$6 x + 6 \cdot - 3 x^{2} + 1 \cdot 1 + 1 (- 3 x)$

Step 2.1.4

Multiply $6$ by $- 3$ .

$6 x - 18 x^{2} + 1 \cdot 1 + 1 (- 3 x)$

Step 2.1.5

Multiply $1$ by $1$ .

$6 x - 18 x^{2} + 1 + 1 (- 3 x)$

Step 2.1.6

Multiply $- 3 x$ by $1$ .

$6 x - 18 x^{2} + 1 - 3 x$

Step 2.2

Subtract $3 x$ from $6 x$ .

$3 x - 18 x^{2} + 1$