Simplify (4a)/5(10a-25b)

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

Step 1

Simplify by multiplying through.

Apply the distributive property.

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

Reorder.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify each term.

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $2$ .

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 25$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $4$ by $- 5$ .

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