Algebra Examples

$(2 x^{2} + 5 a^{2} y) (2 x^{2} - 5 a^{2} y)$

Step 1

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

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Step 1.1

Apply the distributive property.

$2 x^{2} (2 x^{2} - 5 a^{2} y) + 5 a^{2} y (2 x^{2} - 5 a^{2} y)$

Step 1.2

Apply the distributive property.

$2 x^{2} (2 x^{2}) + 2 x^{2} (- 5 a^{2} y) + 5 a^{2} y (2 x^{2} - 5 a^{2} y)$

Step 1.3

Apply the distributive property.

$2 x^{2} (2 x^{2}) + 2 x^{2} (- 5 a^{2} y) + 5 a^{2} y (2 x^{2}) + 5 a^{2} y (- 5 a^{2} y)$

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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

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

Step 2.1.2.2

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

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

Step 2.1.2.3

Add $2$ and $2$ .

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

Step 2.1.3

Multiply $2$ by $2$ .

$4 x^{4} + 2 x^{2} (- 5 a^{2} y) + 5 a^{2} y (2 x^{2}) + 5 a^{2} y (- 5 a^{2} y)$

Step 2.1.4

Multiply $- 5$ by $2$ .

$4 x^{4} - 10 x^{2} (a^{2} y) + 5 a^{2} y (2 x^{2}) + 5 a^{2} y (- 5 a^{2} y)$

Step 2.1.5

Multiply $2$ by $5$ .

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} + 5 a^{2} y (- 5 a^{2} y)$

Step 2.1.6

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

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Step 2.1.6.1

Move $a^{2}$ .

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} + 5 (a^{2} a^{2}) y (- 5 y)$

Step 2.1.6.2

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

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} + 5 a^{2 + 2} y (- 5 y)$

Step 2.1.6.3

Add $2$ and $2$ .

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} + 5 a^{4} y (- 5 y)$

Step 2.1.7

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1.7.1

Move $y$ .

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} + 5 a^{4} (y \cdot y) \cdot - 5$

Step 2.1.7.2

Multiply $y$ by $y$ .

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} + 5 a^{4} y^{2} \cdot - 5$

Step 2.1.8

Multiply $- 5$ by $5$ .

$4 x^{4} - 10 x^{2} a^{2} y + 10 a^{2} y x^{2} - 25 a^{4} y^{2}$

Step 2.2

Move $y$ .

$4 x^{4} - 10 a^{2} x^{2} y + 10 a^{2} x^{2} y - 25 a^{4} y^{2}$

Step 2.3

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

$4 x^{4} + 0 - 25 a^{4} y^{2}$

Step 2.4

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

$4 x^{4} - 25 a^{4} y^{2}$