Algebra Examples

${(- 2 x + 5)}^{2} + (- 2 x + 5) + 10$

Step 1

Remove parentheses.

${(- 2 x + 5)}^{2} - 2 x + 5 + 10$

Step 2

Simplify each term.

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Step 2.1

Rewrite ${(- 2 x + 5)}^{2}$ as $(- 2 x + 5) (- 2 x + 5)$ .

$(- 2 x + 5) (- 2 x + 5) - 2 x + 5 + 10$

Step 2.2

Expand $(- 2 x + 5) (- 2 x + 5)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$- 2 x (- 2 x + 5) + 5 (- 2 x + 5) - 2 x + 5 + 10$

Step 2.2.2

Apply the distributive property.

$- 2 x (- 2 x) - 2 x \cdot 5 + 5 (- 2 x + 5) - 2 x + 5 + 10$

Step 2.2.3

Apply the distributive property.

$- 2 x (- 2 x) - 2 x \cdot 5 + 5 (- 2 x) + 5 \cdot 5 - 2 x + 5 + 10$

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

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 2 x \cdot x - 2 x \cdot 5 + 5 (- 2 x) + 5 \cdot 5 - 2 x + 5 + 10$

Step 2.3.1.2

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

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Step 2.3.1.2.1

Move $x$ .

$- 2 \cdot - 2 (x \cdot x) - 2 x \cdot 5 + 5 (- 2 x) + 5 \cdot 5 - 2 x + 5 + 10$

Step 2.3.1.2.2

Multiply $x$ by $x$ .

$- 2 \cdot - 2 x^{2} - 2 x \cdot 5 + 5 (- 2 x) + 5 \cdot 5 - 2 x + 5 + 10$

Step 2.3.1.3

Multiply $- 2$ by $- 2$ .

$4 x^{2} - 2 x \cdot 5 + 5 (- 2 x) + 5 \cdot 5 - 2 x + 5 + 10$

Step 2.3.1.4

Multiply $5$ by $- 2$ .

$4 x^{2} - 10 x + 5 (- 2 x) + 5 \cdot 5 - 2 x + 5 + 10$

Step 2.3.1.5

Multiply $- 2$ by $5$ .

$4 x^{2} - 10 x - 10 x + 5 \cdot 5 - 2 x + 5 + 10$

Step 2.3.1.6

Multiply $5$ by $5$ .

$4 x^{2} - 10 x - 10 x + 25 - 2 x + 5 + 10$

Step 2.3.2

Subtract $10 x$ from $- 10 x$ .

$4 x^{2} - 20 x + 25 - 2 x + 5 + 10$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $2 x$ from $- 20 x$ .

$4 x^{2} - 22 x + 25 + 5 + 10$

Step 3.2

Simplify by adding numbers.

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Step 3.2.1

Add $25$ and $5$ .

$4 x^{2} - 22 x + 30 + 10$

Step 3.2.2

Add $30$ and $10$ .

$4 x^{2} - 22 x + 40$