Finite Math Examples

$(10 y^{2} - 8) (10 y^{2} + 8)$

Step 1

Expand $(10 y^{2} - 8) (10 y^{2} + 8)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$10 y^{2} (10 y^{2} + 8) - 8 (10 y^{2} + 8)$

Step 1.2

Apply the distributive property.

$10 y^{2} (10 y^{2}) + 10 y^{2} \cdot 8 - 8 (10 y^{2} + 8)$

Step 1.3

Apply the distributive property.

$10 y^{2} (10 y^{2}) + 10 y^{2} \cdot 8 - 8 (10 y^{2}) - 8 \cdot 8$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $10 y^{2} (10 y^{2}) + 10 y^{2} \cdot 8 - 8 (10 y^{2}) - 8 \cdot 8$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms $10 y^{2} \cdot 8$ and $- 8 (10 y^{2})$ .

$10 y^{2} (10 y^{2}) + 8 \cdot 10 y^{2} - 8 \cdot 10 y^{2} - 8 \cdot 8$

Step 2.1.2

Subtract $8 \cdot 10 y^{2}$ from $8 \cdot 10 y^{2}$ .

$10 y^{2} (10 y^{2}) + 0 - 8 \cdot 8$

Step 2.1.3

Add $10 y^{2} (10 y^{2})$ and $0$ .

$10 y^{2} (10 y^{2}) - 8 \cdot 8$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Rewrite using the commutative property of multiplication.

$10 \cdot 10 y^{2} y^{2} - 8 \cdot 8$

Step 2.2.2

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

Tap for more steps...

Step 2.2.2.1

Move $y^{2}$ .

$10 \cdot 10 (y^{2} y^{2}) - 8 \cdot 8$

Step 2.2.2.2

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

$10 \cdot 10 y^{2 + 2} - 8 \cdot 8$

Step 2.2.2.3

Add $2$ and $2$ .

$10 \cdot 10 y^{4} - 8 \cdot 8$

Step 2.2.3

Multiply $10$ by $10$ .

$100 y^{4} - 8 \cdot 8$

Step 2.2.4

Multiply $- 8$ by $8$ .

$100 y^{4} - 64$