Algebra Examples

$8 x (2 x^{3} + 3 x - 1) - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Step 1

Simplify $8 x (2 x^{3} + 3 x - 1) - 4 x^{2} (4 x^{2} + 6) + 8$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Simplify.

Tap for more steps...

Step 1.1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.2

Rewrite using the commutative property of multiplication.

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

Step 1.1.2.3

Multiply $- 1$ by $8$ .

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

Step 1.1.3

Simplify each term.

Tap for more steps...

Step 1.1.3.1

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

Tap for more steps...

Step 1.1.3.1.1

Move $x^{3}$ .

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

Step 1.1.3.1.2

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

Tap for more steps...

Step 1.1.3.1.2.1

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

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

Step 1.1.3.1.2.2

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

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

Step 1.1.3.1.3

Add $3$ and $1$ .

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

Step 1.1.3.2

Multiply $8$ by $2$ .

$16 x^{4} + 8 \cdot 3 x \cdot x - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Step 1.1.3.3

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

Tap for more steps...

Step 1.1.3.3.1

Move $x$ .

$16 x^{4} + 8 \cdot 3 (x \cdot x) - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Step 1.1.3.3.2

Multiply $x$ by $x$ .

$16 x^{4} + 8 \cdot 3 x^{2} - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Step 1.1.3.4

Multiply $8$ by $3$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 x^{2} (4 x^{2} + 6) + 8 = 32$

Step 1.1.4

Apply the distributive property.

$16 x^{4} + 24 x^{2} - 8 x - 4 x^{2} (4 x^{2}) - 4 x^{2} \cdot 6 + 8 = 32$

Step 1.1.5

Rewrite using the commutative property of multiplication.

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{2} x^{2} - 4 x^{2} \cdot 6 + 8 = 32$

Step 1.1.6

Multiply $6$ by $- 4$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{2} x^{2} - 24 x^{2} + 8 = 32$

Step 1.1.7

Simplify each term.

Tap for more steps...

Step 1.1.7.1

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

Tap for more steps...

Step 1.1.7.1.1

Move $x^{2}$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 (x^{2} x^{2}) - 24 x^{2} + 8 = 32$

Step 1.1.7.1.2

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

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{2 + 2} - 24 x^{2} + 8 = 32$

Step 1.1.7.1.3

Add $2$ and $2$ .

$16 x^{4} + 24 x^{2} - 8 x - 4 \cdot 4 x^{4} - 24 x^{2} + 8 = 32$

Step 1.1.7.2

Multiply $- 4$ by $4$ .

$16 x^{4} + 24 x^{2} - 8 x - 16 x^{4} - 24 x^{2} + 8 = 32$

Step 1.2

Combine the opposite terms in $16 x^{4} + 24 x^{2} - 8 x - 16 x^{4} - 24 x^{2} + 8$ .

Tap for more steps...

Step 1.2.1

Subtract $16 x^{4}$ from $16 x^{4}$ .

$24 x^{2} - 8 x + 0 - 24 x^{2} + 8 = 32$

Step 1.2.2

Add $24 x^{2} - 8 x$ and $0$ .

$24 x^{2} - 8 x - 24 x^{2} + 8 = 32$

Step 1.2.3

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

$- 8 x + 0 + 8 = 32$

Step 1.2.4

Add $- 8 x$ and $0$ .

$- 8 x + 8 = 32$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.1

Subtract $8$ from both sides of the equation.

$- 8 x = 32 - 8$

Step 2.2

Subtract $8$ from $32$ .

$- 8 x = 24$

Step 3

Divide each term in $- 8 x = 24$ by $- 8$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $- 8 x = 24$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{24}{- 8}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $24$ by $- 8$ .

$x = - 3$