Simplify 2a^2(3a-5)-6a(8a^2-2a+4)

$2 a^{2} (3 a - 5) - 6 a (8 a^{2} - 2 a + 4)$

Step 1

Simplify each term.

Apply the distributive property.

$2 a^{2} (3 a) + 2 a^{2} \cdot - 5 - 6 a (8 a^{2} - 2 a + 4)$

Rewrite using the commutative property of multiplication.

$2 \cdot 3 a^{2} a + 2 a^{2} \cdot - 5 - 6 a (8 a^{2} - 2 a + 4)$

Multiply $- 5$ by $2$ .

$2 \cdot 3 a^{2} a - 10 a^{2} - 6 a (8 a^{2} - 2 a + 4)$

Simplify each term.

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

Move $a$ .

$2 \cdot 3 (a \cdot a^{2}) - 10 a^{2} - 6 a (8 a^{2} - 2 a + 4)$

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

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

$2 \cdot 3 (a^{1} a^{2}) - 10 a^{2} - 6 a (8 a^{2} - 2 a + 4)$

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

$2 \cdot 3 a^{1 + 2} - 10 a^{2} - 6 a (8 a^{2} - 2 a + 4)$

Add $1$ and $2$ .

$2 \cdot 3 a^{3} - 10 a^{2} - 6 a (8 a^{2} - 2 a + 4)$

Multiply $2$ by $3$ .

$6 a^{3} - 10 a^{2} - 6 a (8 a^{2} - 2 a + 4)$

Apply the distributive property.

$6 a^{3} - 10 a^{2} - 6 a (8 a^{2}) - 6 a (- 2 a) - 6 a \cdot 4$

Simplify.

Rewrite using the commutative property of multiplication.

$6 a^{3} - 10 a^{2} - 6 \cdot 8 a \cdot a^{2} - 6 a (- 2 a) - 6 a \cdot 4$

Rewrite using the commutative property of multiplication.

$6 a^{3} - 10 a^{2} - 6 \cdot 8 a \cdot a^{2} - 6 \cdot - 2 a \cdot a - 6 a \cdot 4$

Multiply $4$ by $- 6$ .

$6 a^{3} - 10 a^{2} - 6 \cdot 8 a \cdot a^{2} - 6 \cdot - 2 a \cdot a - 24 a$

Simplify each term.

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

Move $a^{2}$ .

$6 a^{3} - 10 a^{2} - 6 \cdot 8 (a^{2} a) - 6 \cdot - 2 a \cdot a - 24 a$

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

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

$6 a^{3} - 10 a^{2} - 6 \cdot 8 (a^{2} a^{1}) - 6 \cdot - 2 a \cdot a - 24 a$

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

$6 a^{3} - 10 a^{2} - 6 \cdot 8 a^{2 + 1} - 6 \cdot - 2 a \cdot a - 24 a$

Add $2$ and $1$ .

$6 a^{3} - 10 a^{2} - 6 \cdot 8 a^{3} - 6 \cdot - 2 a \cdot a - 24 a$

Multiply $- 6$ by $8$ .

$6 a^{3} - 10 a^{2} - 48 a^{3} - 6 \cdot - 2 a \cdot a - 24 a$

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

Move $a$ .

$6 a^{3} - 10 a^{2} - 48 a^{3} - 6 \cdot - 2 (a \cdot a) - 24 a$

Multiply $a$ by $a$ .

$6 a^{3} - 10 a^{2} - 48 a^{3} - 6 \cdot - 2 a^{2} - 24 a$

Multiply $- 6$ by $- 2$ .

$6 a^{3} - 10 a^{2} - 48 a^{3} + 12 a^{2} - 24 a$

Step 2

Simplify by adding terms.

Subtract $48 a^{3}$ from $6 a^{3}$ .

$- 42 a^{3} - 10 a^{2} + 12 a^{2} - 24 a$

Add $- 10 a^{2}$ and $12 a^{2}$ .

$- 42 a^{3} + 2 a^{2} - 24 a$

Simplify 2a^2(3a-5)-6a(8a^2-2a+4)

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