Simplify 1/28x(10x^3+6x-8)-1/26x(8x^3+2x-4)

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

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $8 x (10 x^{3} + 6 x - 8)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 8$ by $4$ .

$4 \cdot 10 x \cdot x^{3} + 4 \cdot 6 x \cdot x - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Simplify each term.

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

Move $x^{3}$ .

$4 \cdot 10 (x^{3} x) + 4 \cdot 6 x \cdot x - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Multiply $x^{3}$ by $x$ .

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

$4 \cdot 10 (x^{3} x^{1}) + 4 \cdot 6 x \cdot x - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

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

$4 \cdot 10 x^{3 + 1} + 4 \cdot 6 x \cdot x - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Add $3$ and $1$ .

$4 \cdot 10 x^{4} + 4 \cdot 6 x \cdot x - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Multiply $4$ by $10$ .

$40 x^{4} + 4 \cdot 6 x \cdot x - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$40 x^{4} + 4 \cdot 6 (x \cdot x) - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Multiply $x$ by $x$ .

$40 x^{4} + 4 \cdot 6 x^{2} - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Multiply $4$ by $6$ .

$40 x^{4} + 24 x^{2} - 32 x - \frac{1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$40 x^{4} + 24 x^{2} - 32 x + \frac{- 1}{2} \cdot (6 x (8 x^{3} + 2 x - 4))$

Factor $2$ out of $6 x (8 x^{3} + 2 x - 4)$ .

$40 x^{4} + 24 x^{2} - 32 x + \frac{- 1}{2} \cdot (2 (3 x (8 x^{3} + 2 x - 4)))$

Cancel the common factor.

$40 x^{4} + 24 x^{2} - 32 x + \frac{- 1}{2} \cdot (2 (3 x (8 x^{3} + 2 x - 4)))$

Rewrite the expression.

$40 x^{4} + 24 x^{2} - 32 x - 1 \cdot (3 x (8 x^{3} + 2 x - 4))$

Multiply $3$ by $- 1$ .

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (x (8 x^{3} + 2 x - 4))$

Apply the distributive property.

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (x (8 x^{3}) + x (2 x) + x \cdot - 4)$

Simplify.

Rewrite using the commutative property of multiplication.

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x \cdot x^{3} + x (2 x) + x \cdot - 4)$

Rewrite using the commutative property of multiplication.

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x \cdot x^{3} + 2 x \cdot x + x \cdot - 4)$

Move $- 4$ to the left of $x$ .

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x \cdot x^{3} + 2 x \cdot x - 4 \cdot x)$

Simplify each term.

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

Move $x^{3}$ .

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 (x^{3} x) + 2 x \cdot x - 4 \cdot x)$

Multiply $x^{3}$ by $x$ .

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

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 (x^{3} x^{1}) + 2 x \cdot x - 4 \cdot x)$

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

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x^{3 + 1} + 2 x \cdot x - 4 \cdot x)$

Add $3$ and $1$ .

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x^{4} + 2 x \cdot x - 4 \cdot x)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x^{4} + 2 (x \cdot x) - 4 \cdot x)$

Multiply $x$ by $x$ .

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x^{4} + 2 x^{2} - 4 \cdot x)$

$40 x^{4} + 24 x^{2} - 32 x - 3 \cdot (8 x^{4} + 2 x^{2} - 4 x)$

Apply the distributive property.

$40 x^{4} + 24 x^{2} - 32 x - 3 (8 x^{4}) - 3 (2 x^{2}) - 3 (- 4 x)$

Simplify.

Multiply $8$ by $- 3$ .

$40 x^{4} + 24 x^{2} - 32 x - 24 x^{4} - 3 (2 x^{2}) - 3 (- 4 x)$

Multiply $2$ by $- 3$ .

$40 x^{4} + 24 x^{2} - 32 x - 24 x^{4} - 6 x^{2} - 3 (- 4 x)$

Multiply $- 4$ by $- 3$ .

$40 x^{4} + 24 x^{2} - 32 x - 24 x^{4} - 6 x^{2} + 12 x$

Simplify by adding terms.

Subtract $24 x^{4}$ from $40 x^{4}$ .

$16 x^{4} + 24 x^{2} - 32 x - 6 x^{2} + 12 x$

Subtract $6 x^{2}$ from $24 x^{2}$ .

$16 x^{4} + 18 x^{2} - 32 x + 12 x$

Add $- 32 x$ and $12 x$ .

$16 x^{4} + 18 x^{2} - 20 x$

Simplify 1/2*8x(10x^3+6x-8)-1/2*6x(8x^3+2x-4)

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Simplify 1/28x(10x^3+6x-8)-1/26x(8x^3+2x-4)