Basic Math Examples

${(2 a - 5)}^{2}$

Step 1

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

$(2 a - 5) (2 a - 5)$

Step 2

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

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Step 2.1

Apply the distributive property.

$2 a (2 a - 5) - 5 (2 a - 5)$

Step 2.2

Apply the distributive property.

$2 a (2 a) + 2 a \cdot - 5 - 5 (2 a - 5)$

Step 2.3

Apply the distributive property.

$2 a (2 a) + 2 a \cdot - 5 - 5 (2 a) - 5 \cdot - 5$

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

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a \cdot - 5 - 5 (2 a) - 5 \cdot - 5$

Step 3.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1.2.1

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a \cdot - 5 - 5 (2 a) - 5 \cdot - 5$

Step 3.1.2.2

Multiply $a$ by $a$ .

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

Step 3.1.3

Multiply $2$ by $2$ .

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

Step 3.1.4

Multiply $- 5$ by $2$ .

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

Step 3.1.5

Multiply $2$ by $- 5$ .

$4 a^{2} - 10 a - 10 a - 5 \cdot - 5$

Step 3.1.6

Multiply $- 5$ by $- 5$ .

$4 a^{2} - 10 a - 10 a + 25$

Step 3.2

Subtract $10 a$ from $- 10 a$ .

$4 a^{2} - 20 a + 25$