Algebra Examples

$(2 x + 7) (x - 1) = 0$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

Step 2

Expand $(2 x + 7) (x - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$2 x (x - 1) + 7 (x - 1) = 0$

Step 2.2

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 7 (x - 1) = 0$

Step 2.3

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 1 + 7 x + 7 \cdot - 1 = 0$

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

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

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Step 3.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 1 + 7 x + 7 \cdot - 1 = 0$

Step 3.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 1 + 7 x + 7 \cdot - 1 = 0$

Step 3.1.2

Multiply $- 1$ by $2$ .

$2 x^{2} - 2 x + 7 x + 7 \cdot - 1 = 0$

Step 3.1.3

Multiply $7$ by $- 1$ .

$2 x^{2} - 2 x + 7 x - 7 = 0$

Step 3.2

Add $- 2 x$ and $7 x$ .

$2 x^{2} + 5 x - 7 = 0$

Step 4