Algebra Examples

${(x - 4)}^{2} - 5 (x - 4) - 3$

Step 1

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

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

Step 2

Simplify each term.

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Step 2.1

Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$(x - 4) (x - 4) - 5 (x - 4) - 3$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$x (x - 4) - 4 (x - 4) - 5 (x - 4) - 3$

Step 2.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 4 (x - 4) - 5 (x - 4) - 3$

Step 2.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4 - 5 (x - 4) - 3$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4 - 5 (x - 4) - 3$

Step 2.3.1.2

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4 - 5 (x - 4) - 3$

Step 2.3.1.3

Multiply $- 4$ by $- 4$ .

$x^{2} - 4 x - 4 x + 16 - 5 (x - 4) - 3$

Step 2.3.2

Subtract $4 x$ from $- 4 x$ .

$x^{2} - 8 x + 16 - 5 (x - 4) - 3$

Step 2.4

Apply the distributive property.

$x^{2} - 8 x + 16 - 5 x - 5 \cdot - 4 - 3$

Step 2.5

Multiply $- 5$ by $- 4$ .

$x^{2} - 8 x + 16 - 5 x + 20 - 3$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $5 x$ from $- 8 x$ .

$x^{2} - 13 x + 16 + 20 - 3$

Step 3.2

Simplify by adding and subtracting.

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Step 3.2.1

Add $16$ and $20$ .

$x^{2} - 13 x + 36 - 3$

Step 3.2.2

Subtract $3$ from $36$ .

$x^{2} - 13 x + 33$