Pre-Algebra Examples

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

Step 1

Expand $(6 x^{2} + 4) (8 x - 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2

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

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Step 2.2.1

Move $x$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $1$ and $2$ .

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

Step 2.3

Multiply $6$ by $8$ .

$48 x^{3} + 6 x^{2} \cdot - 3 + 4 (8 x) + 4 \cdot - 3$

Step 2.4

Multiply $- 3$ by $6$ .

$48 x^{3} - 18 x^{2} + 4 (8 x) + 4 \cdot - 3$

Step 2.5

Multiply $8$ by $4$ .

$48 x^{3} - 18 x^{2} + 32 x + 4 \cdot - 3$

Step 2.6

Multiply $4$ by $- 3$ .

$48 x^{3} - 18 x^{2} + 32 x - 12$