Algebra Examples

$y = - 2 (2 x + 1) (x - 3) + 5$

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$y = (- 2 (2 x) - 2 \cdot 1) (x - 3) + 5$

Step 2.2

Multiply $2$ by $- 2$ .

$y = (- 4 x - 2 \cdot 1) (x - 3) + 5$

Step 2.3

Multiply $- 2$ by $1$ .

$y = (- 4 x - 2) (x - 3) + 5$

Step 2.4

Expand $(- 4 x - 2) (x - 3)$ using the FOIL Method.

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Step 2.4.1

Apply the distributive property.

$y = - 4 x (x - 3) - 2 (x - 3) + 5$

Step 2.4.2

Apply the distributive property.

$y = - 4 x \cdot x - 4 x \cdot - 3 - 2 (x - 3) + 5$

Step 2.4.3

Apply the distributive property.

$y = - 4 x \cdot x - 4 x \cdot - 3 - 2 x - 2 \cdot - 3 + 5$

Step 2.5

Simplify and combine like terms.

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Step 2.5.1

Simplify each term.

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Step 2.5.1.1

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

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Step 2.5.1.1.1

Move $x$ .

$y = - 4 (x \cdot x) - 4 x \cdot - 3 - 2 x - 2 \cdot - 3 + 5$

Step 2.5.1.1.2

Multiply $x$ by $x$ .

$y = - 4 x^{2} - 4 x \cdot - 3 - 2 x - 2 \cdot - 3 + 5$

Step 2.5.1.2

Multiply $- 3$ by $- 4$ .

$y = - 4 x^{2} + 12 x - 2 x - 2 \cdot - 3 + 5$

Step 2.5.1.3

Multiply $- 2$ by $- 3$ .

$y = - 4 x^{2} + 12 x - 2 x + 6 + 5$

Step 2.5.2

Subtract $2 x$ from $12 x$ .

$y = - 4 x^{2} + 10 x + 6 + 5$

Step 3

Add $6$ and $5$ .

$y = - 4 x^{2} + 10 x + 11$

Step 4