Find the Product 7a(6-2a-a^2)

$7 a (6 - 2 a - a^{2})$

Step 1

Apply the distributive property.

$7 a \cdot 6 + 7 a (- 2 a) + 7 a (- a^{2})$

Step 2

Simplify.

Multiply $6$ by $7$ .

$42 a + 7 a (- 2 a) + 7 a (- a^{2})$

Rewrite using the commutative property of multiplication.

$42 a + 7 \cdot - 2 a \cdot a + 7 a (- a^{2})$

Rewrite using the commutative property of multiplication.

$42 a + 7 \cdot - 2 a \cdot a + 7 \cdot - 1 a \cdot a^{2}$

Step 3

Simplify each term.

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

Move $a$ .

$42 a + 7 \cdot - 2 (a \cdot a) + 7 \cdot - 1 a \cdot a^{2}$

Multiply $a$ by $a$ .

$42 a + 7 \cdot - 2 a^{2} + 7 \cdot - 1 a \cdot a^{2}$

Multiply $7$ by $- 2$ .

$42 a - 14 a^{2} + 7 \cdot - 1 a \cdot a^{2}$

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

Move $a^{2}$ .

$42 a - 14 a^{2} + 7 \cdot - 1 (a^{2} a)$

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

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

$42 a - 14 a^{2} + 7 \cdot - 1 (a^{2} a^{1})$

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

$42 a - 14 a^{2} + 7 \cdot - 1 a^{2 + 1}$

Add $2$ and $1$ .

$42 a - 14 a^{2} + 7 \cdot - 1 a^{3}$

Multiply $7$ by $- 1$ .

$42 a - 14 a^{2} - 7 a^{3}$