Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

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

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $10$ by $10$ .

$100 x^{2} + 10 x (- y^{2}) + y^{2} (10 x) + y^{2} (- y^{2})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$100 x^{2} + 10 \cdot - 1 x y^{2} + y^{2} (10 x) + y^{2} (- y^{2})$

Step 2.1.5

Multiply $10$ by $- 1$ .

$100 x^{2} - 10 x y^{2} + y^{2} (10 x) + y^{2} (- y^{2})$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$100 x^{2} - 10 x y^{2} + 10 y^{2} x + y^{2} (- y^{2})$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$100 x^{2} - 10 x y^{2} + 10 y^{2} x - y^{2} y^{2}$

Step 2.1.8

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

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Step 2.1.8.1

Move $y^{2}$ .

$100 x^{2} - 10 x y^{2} + 10 y^{2} x - (y^{2} y^{2})$

Step 2.1.8.2

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

$100 x^{2} - 10 x y^{2} + 10 y^{2} x - y^{2 + 2}$

Step 2.1.8.3

Add $2$ and $2$ .

$100 x^{2} - 10 x y^{2} + 10 y^{2} x - y^{4}$

Step 2.2

Add $- 10 x y^{2}$ and $10 y^{2} x$ .

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Step 2.2.1

Move $y^{2}$ .

$100 x^{2} - 10 x y^{2} + 10 x y^{2} - y^{4}$

Step 2.2.2

Add $- 10 x y^{2}$ and $10 x y^{2}$ .

$100 x^{2} + 0 - y^{4}$

Step 2.3

Add $100 x^{2}$ and $0$ .

$100 x^{2} - y^{4}$