Solve 2(a ^ 2 - b ^ 2) - 3[a ^ 2 - \{b ^ 2 - a ^ 2 + (a ^ 2 - b ^ 2 - a ^ 2)\}]

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Question

$$2(a^{2}-b^{2})-3[a^{2}-\{b^{2}-a^{2}+(a^{2}-b^{2}-a^{2})\}]$$

Evaluate

$-4a^{2}-2b^{2}$

Solution Steps

Use the distributive property to multiply $2$ by $a^{2}-b^{2}$.

$$2a^{2}-2b^{2}-3\left(a^{2}-\left(b^{2}-a^{2}+a^{2}-b^{2}-a^{2}\right)\right)$$

Combine $-a^{2}$ and $a^{2}$ to get $0$.

$$2a^{2}-2b^{2}-3\left(a^{2}-\left(b^{2}-b^{2}-a^{2}\right)\right)$$

Combine $b^{2}$ and $-b^{2}$ to get $0$.

$$2a^{2}-2b^{2}-3\left(a^{2}-\left(-a^{2}\right)\right)$$

The opposite of $-a^{2}$ is $a^{2}$.

$$2a^{2}-2b^{2}-3\left(a^{2}+a^{2}\right)$$

Combine $a^{2}$ and $a^{2}$ to get $2a^{2}$.

$$2a^{2}-2b^{2}-3\times 2a^{2}$$

Multiply $3$ and $2$ to get $6$.

$$2a^{2}-2b^{2}-6a^{2}$$

Combine $2a^{2}$ and $-6a^{2}$ to get $-4a^{2}$.

$$-4a^{2}-2b^{2}$$

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$-4a^{2}-2b^{2}$

Solution Steps

Use the distributive property to multiply $2$ by $a^{2}-b^{2}$.

$$2a^{2}-2b^{2}-3\left(a^{2}-\left(b^{2}-a^{2}+a^{2}-b^{2}-a^{2}\right)\right)$$

Combine $-a^{2}$ and $a^{2}$ to get $0$.

$$2a^{2}-2b^{2}-3\left(a^{2}-\left(b^{2}-b^{2}-a^{2}\right)\right)$$

Combine $b^{2}$ and $-b^{2}$ to get $0$.

$$2a^{2}-2b^{2}-3\left(a^{2}-\left(-a^{2}\right)\right)$$

The opposite of $-a^{2}$ is $a^{2}$.

$$2a^{2}-2b^{2}-3\left(a^{2}+a^{2}\right)$$

Combine $a^{2}$ and $a^{2}$ to get $2a^{2}$.

$$2a^{2}-2b^{2}-3\times 2a^{2}$$

Multiply $3$ and $2$ to get $6$.

$$2a^{2}-2b^{2}-6a^{2}$$

Combine $2a^{2}$ and $-6a^{2}$ to get $-4a^{2}$.

$$-4a^{2}-2b^{2}$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

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Linear Algebra

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Example

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Solution Steps