Algebra Examples

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

Step 1

Expand $(3 x^{2} - 4) (x^{2} - 8 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $x^{2}$ .

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

Step 2.1.1.2

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

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

Step 2.1.1.3

Add $2$ and $2$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

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

Step 2.1.3.2

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

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Step 2.1.3.2.1

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

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

Step 2.1.3.2.2

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

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

Step 2.1.3.3

Add $1$ and $2$ .

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

Step 2.1.4

Multiply $3$ by $- 8$ .

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

Step 2.1.5

Multiply $4$ by $3$ .

$3 x^{4} - 24 x^{3} + 12 x^{2} - 4 x^{2} - 4 (- 8 x) - 4 \cdot 4$

Step 2.1.6

Multiply $- 8$ by $- 4$ .

$3 x^{4} - 24 x^{3} + 12 x^{2} - 4 x^{2} + 32 x - 4 \cdot 4$

Step 2.1.7

Multiply $- 4$ by $4$ .

$3 x^{4} - 24 x^{3} + 12 x^{2} - 4 x^{2} + 32 x - 16$

Step 2.2

Subtract $4 x^{2}$ from $12 x^{2}$ .

$3 x^{4} - 24 x^{3} + 8 x^{2} + 32 x - 16$