Algebra Examples

$\frac{4 a}{5} (10 a - 25 b)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$\frac{4 a}{5} (10 a) + \frac{4 a}{5} (- 25 b)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$10 \frac{4 a}{5} a + \frac{4 a}{5} (- 25 b)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$10 \frac{4 a}{5} a - 25 \frac{4 a}{5} b$

$10 \frac{4 a}{5} a - 25 \frac{4 a}{5} b$

$10 \frac{4 a}{5} a - 25 \frac{4 a}{5} b$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $5$ .

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Step 2.1.1

Factor $5$ out of $10$ .

$5 (2) \frac{4 a}{5} a - 25 \frac{4 a}{5} b$

Step 2.1.2

Cancel the common factor.

$5 \cdot 2 \frac{4 a}{5} a - 25 \frac{4 a}{5} b$

Step 2.1.3

Rewrite the expression.

$2 (4 a) a - 25 \frac{4 a}{5} b$

$2 (4 a) a - 25 \frac{4 a}{5} b$

Step 2.2

Multiply $4$ by $2$ .

$8 a \cdot a - 25 \frac{4 a}{5} b$

Step 2.3

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

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Step 2.3.1

Move $a$ .

$8 (a \cdot a) - 25 \frac{4 a}{5} b$

Step 2.3.2

Multiply $a$ by $a$ .

$8 a^{2} - 25 \frac{4 a}{5} b$

$8 a^{2} - 25 \frac{4 a}{5} b$

Step 2.4

Cancel the common factor of $5$ .

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Step 2.4.1

Factor $5$ out of $- 25$ .

$8 a^{2} + 5 (- 5) \frac{4 a}{5} b$

Step 2.4.2

Cancel the common factor.

$8 a^{2} + 5 \cdot - 5 \frac{4 a}{5} b$

Step 2.4.3

Rewrite the expression.

$8 a^{2} - 5 (4 a) b$

$8 a^{2} - 5 (4 a) b$

Step 2.5

Multiply $4$ by $- 5$ .

$8 a^{2} - 20 a b$

$8 a^{2} - 20 a b$

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