Algebra Examples

$5 x - 3 {(x - 1)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$5 x - 3 ((x - 1) (x - 1))$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$5 x - 3 (x (x - 1) - 1 (x - 1))$

Step 1.2.2

Apply the distributive property.

$5 x - 3 (x \cdot x + x \cdot - 1 - 1 (x - 1))$

Step 1.2.3

Apply the distributive property.

$5 x - 3 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1)$

$5 x - 3 (x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$5 x - 3 (x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1)$

Step 1.3.1.2

Move $- 1$ to the left of $x$ .

$5 x - 3 (x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1)$

Step 1.3.1.3

Rewrite $- 1 x$ as $- x$ .

$5 x - 3 (x^{2} - x - 1 x - 1 \cdot - 1)$

Step 1.3.1.4

Rewrite $- 1 x$ as $- x$ .

$5 x - 3 (x^{2} - x - x - 1 \cdot - 1)$

Step 1.3.1.5

Multiply $- 1$ by $- 1$ .

$5 x - 3 (x^{2} - x - x + 1)$

$5 x - 3 (x^{2} - x - x + 1)$

Step 1.3.2

Subtract $x$ from $- x$ .

$5 x - 3 (x^{2} - 2 x + 1)$

$5 x - 3 (x^{2} - 2 x + 1)$

Step 1.4

Apply the distributive property.

$5 x - 3 x^{2} - 3 (- 2 x) - 3 \cdot 1$

Step 1.5

Simplify.

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Step 1.5.1

Multiply $- 2$ by $- 3$ .

$5 x - 3 x^{2} + 6 x - 3 \cdot 1$

Step 1.5.2

Multiply $- 3$ by $1$ .

$5 x - 3 x^{2} + 6 x - 3$

$5 x - 3 x^{2} + 6 x - 3$

$5 x - 3 x^{2} + 6 x - 3$

Step 2

Add $5 x$ and $6 x$ .

$- 3 x^{2} + 11 x - 3$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$