Simplify 7x^4(2x^6+4x^3-3x^2-5x)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

Multiply $x^{4}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

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

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

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

Add $6$ and $4$ .

$7 \cdot 2 x^{10} + 7 \cdot 4 x^{4} x^{3} + 7 \cdot - 3 x^{4} x^{2} + 7 \cdot - 5 x^{4} x$

Multiply $7$ by $2$ .

$14 x^{10} + 7 \cdot 4 x^{4} x^{3} + 7 \cdot - 3 x^{4} x^{2} + 7 \cdot - 5 x^{4} x$

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

Move $x^{3}$ .

$14 x^{10} + 7 \cdot 4 (x^{3} x^{4}) + 7 \cdot - 3 x^{4} x^{2} + 7 \cdot - 5 x^{4} x$

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

$14 x^{10} + 7 \cdot 4 x^{3 + 4} + 7 \cdot - 3 x^{4} x^{2} + 7 \cdot - 5 x^{4} x$

Add $3$ and $4$ .

$14 x^{10} + 7 \cdot 4 x^{7} + 7 \cdot - 3 x^{4} x^{2} + 7 \cdot - 5 x^{4} x$

Multiply $7$ by $4$ .

$14 x^{10} + 28 x^{7} + 7 \cdot - 3 x^{4} x^{2} + 7 \cdot - 5 x^{4} x$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$14 x^{10} + 28 x^{7} + 7 \cdot - 3 (x^{2} x^{4}) + 7 \cdot - 5 x^{4} x$

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

$14 x^{10} + 28 x^{7} + 7 \cdot - 3 x^{2 + 4} + 7 \cdot - 5 x^{4} x$

Add $2$ and $4$ .

$14 x^{10} + 28 x^{7} + 7 \cdot - 3 x^{6} + 7 \cdot - 5 x^{4} x$

Multiply $7$ by $- 3$ .

$14 x^{10} + 28 x^{7} - 21 x^{6} + 7 \cdot - 5 x^{4} x$

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

Move $x$ .

$14 x^{10} + 28 x^{7} - 21 x^{6} + 7 \cdot - 5 (x \cdot x^{4})$

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

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

$14 x^{10} + 28 x^{7} - 21 x^{6} + 7 \cdot - 5 (x^{1} x^{4})$

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

$14 x^{10} + 28 x^{7} - 21 x^{6} + 7 \cdot - 5 x^{1 + 4}$

Add $1$ and $4$ .

$14 x^{10} + 28 x^{7} - 21 x^{6} + 7 \cdot - 5 x^{5}$

Multiply $7$ by $- 5$ .

$14 x^{10} + 28 x^{7} - 21 x^{6} - 35 x^{5}$

Simplify 7x^4(2x^6+4x^3-3x^2-5x)

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