Basic Math Examples

${((a^{2} + b^{2}) - (a^{2} - b^{2}))}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

${(a^{2} + b^{2} - a^{2} - - b^{2})}^{2}$

Step 1.2

Multiply $- - b^{2}$ .

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Step 1.2.1

Multiply $- 1$ by $- 1$ .

${(a^{2} + b^{2} - a^{2} + 1 b^{2})}^{2}$

Step 1.2.2

Multiply $b^{2}$ by $1$ .

${(a^{2} + b^{2} - a^{2} + b^{2})}^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $a^{2} + b^{2} - a^{2} + b^{2}$ .

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Step 2.1.1

Subtract $a^{2}$ from $a^{2}$ .

${(b^{2} + 0 + b^{2})}^{2}$

Step 2.1.2

Add $b^{2}$ and $0$ .

${(b^{2} + b^{2})}^{2}$

Step 2.2

Add $b^{2}$ and $b^{2}$ .

${(2 b^{2})}^{2}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Apply the product rule to $2 b^{2}$ .

$2^{2} {(b^{2})}^{2}$

Step 2.3.2

Raise $2$ to the power of $2$ .

$4 {(b^{2})}^{2}$

Step 2.3.3

Multiply the exponents in ${(b^{2})}^{2}$ .

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Step 2.3.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 b^{2 \cdot 2}$

Step 2.3.3.2

Multiply $2$ by $2$ .

$4 b^{4}$