Simplify -9x^2(2x^5+4x^3-2x)-3x^4(2x^3-5x+6)

$- 9 x^{2} (2 x^{5} + 4 x^{3} - 2 x) - 3 x^{4} (2 x^{3} - 5 x + 6)$

Step 1

Simplify each term.

Apply the distributive property.

$- 9 x^{2} (2 x^{5}) - 9 x^{2} (4 x^{3}) - 9 x^{2} (- 2 x) - 3 x^{4} (2 x^{3} - 5 x + 6)$

Simplify.

Rewrite using the commutative property of multiplication.

$- 9 \cdot 2 x^{2} x^{5} - 9 x^{2} (4 x^{3}) - 9 x^{2} (- 2 x) - 3 x^{4} (2 x^{3} - 5 x + 6)$

Rewrite using the commutative property of multiplication.

$- 9 \cdot 2 x^{2} x^{5} - 9 \cdot 4 x^{2} x^{3} - 9 x^{2} (- 2 x) - 3 x^{4} (2 x^{3} - 5 x + 6)$

Rewrite using the commutative property of multiplication.

$- 9 \cdot 2 x^{2} x^{5} - 9 \cdot 4 x^{2} x^{3} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

Simplify each term.

Multiply $x^{2}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$- 9 \cdot 2 (x^{5} x^{2}) - 9 \cdot 4 x^{2} x^{3} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

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

$- 9 \cdot 2 x^{5 + 2} - 9 \cdot 4 x^{2} x^{3} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

Add $5$ and $2$ .

$- 9 \cdot 2 x^{7} - 9 \cdot 4 x^{2} x^{3} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

Multiply $- 9$ by $2$ .

$- 18 x^{7} - 9 \cdot 4 x^{2} x^{3} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 18 x^{7} - 9 \cdot 4 (x^{3} x^{2}) - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

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

$- 18 x^{7} - 9 \cdot 4 x^{3 + 2} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

Add $3$ and $2$ .

$- 18 x^{7} - 9 \cdot 4 x^{5} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

Multiply $- 9$ by $4$ .

$- 18 x^{7} - 36 x^{5} - 9 \cdot - 2 x^{2} x - 3 x^{4} (2 x^{3} - 5 x + 6)$

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

Move $x$ .

$- 18 x^{7} - 36 x^{5} - 9 \cdot - 2 (x \cdot x^{2}) - 3 x^{4} (2 x^{3} - 5 x + 6)$

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

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

$- 18 x^{7} - 36 x^{5} - 9 \cdot - 2 (x^{1} x^{2}) - 3 x^{4} (2 x^{3} - 5 x + 6)$

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

$- 18 x^{7} - 36 x^{5} - 9 \cdot - 2 x^{1 + 2} - 3 x^{4} (2 x^{3} - 5 x + 6)$

Add $1$ and $2$ .

$- 18 x^{7} - 36 x^{5} - 9 \cdot - 2 x^{3} - 3 x^{4} (2 x^{3} - 5 x + 6)$

Multiply $- 9$ by $- 2$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 x^{4} (2 x^{3} - 5 x + 6)$

Apply the distributive property.

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 x^{4} (2 x^{3}) - 3 x^{4} (- 5 x) - 3 x^{4} \cdot 6$

Simplify.

Rewrite using the commutative property of multiplication.

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 \cdot 2 x^{4} x^{3} - 3 x^{4} (- 5 x) - 3 x^{4} \cdot 6$

Rewrite using the commutative property of multiplication.

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 \cdot 2 x^{4} x^{3} - 3 \cdot - 5 x^{4} x - 3 x^{4} \cdot 6$

Multiply $6$ by $- 3$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 \cdot 2 x^{4} x^{3} - 3 \cdot - 5 x^{4} x - 18 x^{4}$

Simplify each term.

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 \cdot 2 (x^{3} x^{4}) - 3 \cdot - 5 x^{4} x - 18 x^{4}$

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

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 \cdot 2 x^{3 + 4} - 3 \cdot - 5 x^{4} x - 18 x^{4}$

Add $3$ and $4$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 3 \cdot 2 x^{7} - 3 \cdot - 5 x^{4} x - 18 x^{4}$

Multiply $- 3$ by $2$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 6 x^{7} - 3 \cdot - 5 x^{4} x - 18 x^{4}$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 6 x^{7} - 3 \cdot - 5 (x \cdot x^{4}) - 18 x^{4}$

Multiply $x$ by $x^{4}$ .

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

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 6 x^{7} - 3 \cdot - 5 (x^{1} x^{4}) - 18 x^{4}$

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

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 6 x^{7} - 3 \cdot - 5 x^{1 + 4} - 18 x^{4}$

Add $1$ and $4$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 6 x^{7} - 3 \cdot - 5 x^{5} - 18 x^{4}$

Multiply $- 3$ by $- 5$ .

$- 18 x^{7} - 36 x^{5} + 18 x^{3} - 6 x^{7} + 15 x^{5} - 18 x^{4}$

Step 2

Simplify by adding terms.

Subtract $6 x^{7}$ from $- 18 x^{7}$ .

$- 24 x^{7} - 36 x^{5} + 18 x^{3} + 15 x^{5} - 18 x^{4}$

Add $- 36 x^{5}$ and $15 x^{5}$ .

$- 24 x^{7} - 21 x^{5} + 18 x^{3} - 18 x^{4}$

Move $18 x^{3}$ .

$- 24 x^{7} - 21 x^{5} - 18 x^{4} + 18 x^{3}$

Simplify -9x^2(2x^5+4x^3-2x)-3x^4(2x^3-5x+6)

Related Questions

Support LCMGCF.com by disabling your adblocker.