Expand the Trigonometric Expression -3a(a^2-10a+25)

$- 3 a (a^{2} - 10 a + 25)$

Step 1

Apply the distributive property.

$- 3 a \cdot a^{2} - 3 a (- 10 a) - 3 a \cdot 25$

Step 2

Simplify.

Multiply $a$ by $a^{2}$ by adding the exponents.

Move $a^{2}$ .

$- 3 (a^{2} a) - 3 a (- 10 a) - 3 a \cdot 25$

Multiply $a^{2}$ by $a$ .

Raise $a$ to the power of $1$ .

$- 3 (a^{2} a^{1}) - 3 a (- 10 a) - 3 a \cdot 25$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3 a^{2 + 1} - 3 a (- 10 a) - 3 a \cdot 25$

Add $2$ and $1$ .

$- 3 a^{3} - 3 a (- 10 a) - 3 a \cdot 25$

Rewrite using the commutative property of multiplication.

$- 3 a^{3} - 3 \cdot - 10 a \cdot a - 3 a \cdot 25$

Multiply $25$ by $- 3$ .

$- 3 a^{3} - 3 \cdot - 10 a \cdot a - 75 a$

Step 3

Simplify each term.

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

Move $a$ .

$- 3 a^{3} - 3 \cdot - 10 (a \cdot a) - 75 a$

Multiply $a$ by $a$ .

$- 3 a^{3} - 3 \cdot - 10 a^{2} - 75 a$

Multiply $- 3$ by $- 10$ .

$- 3 a^{3} + 30 a^{2} - 75 a$