Algebra Examples

$(5 x^{2} - 7) (5 x^{2} + 7)$

Step 1

Expand $(5 x^{2} - 7) (5 x^{2} + 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 x^{2} (5 x^{2} + 7) - 7 (5 x^{2} + 7)$

Step 1.2

Apply the distributive property.

$5 x^{2} (5 x^{2}) + 5 x^{2} \cdot 7 - 7 (5 x^{2} + 7)$

Step 1.3

Apply the distributive property.

$5 x^{2} (5 x^{2}) + 5 x^{2} \cdot 7 - 7 (5 x^{2}) - 7 \cdot 7$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x^{2} x^{2} + 5 x^{2} \cdot 7 - 7 (5 x^{2}) - 7 \cdot 7$

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$5 \cdot 5 (x^{2} x^{2}) + 5 x^{2} \cdot 7 - 7 (5 x^{2}) - 7 \cdot 7$

Step 2.1.2.2

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

$5 \cdot 5 x^{2 + 2} + 5 x^{2} \cdot 7 - 7 (5 x^{2}) - 7 \cdot 7$

Step 2.1.2.3

Add $2$ and $2$ .

$5 \cdot 5 x^{4} + 5 x^{2} \cdot 7 - 7 (5 x^{2}) - 7 \cdot 7$

Step 2.1.3

Multiply $5$ by $5$ .

$25 x^{4} + 5 x^{2} \cdot 7 - 7 (5 x^{2}) - 7 \cdot 7$

Step 2.1.4

Multiply $7$ by $5$ .

$25 x^{4} + 35 x^{2} - 7 (5 x^{2}) - 7 \cdot 7$

Step 2.1.5

Multiply $5$ by $- 7$ .

$25 x^{4} + 35 x^{2} - 35 x^{2} - 7 \cdot 7$

Step 2.1.6

Multiply $- 7$ by $7$ .

$25 x^{4} + 35 x^{2} - 35 x^{2} - 49$

Step 2.2

Subtract $35 x^{2}$ from $35 x^{2}$ .

$25 x^{4} + 0 - 49$

Step 2.3

Add $25 x^{4}$ and $0$ .

$25 x^{4} - 49$