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(b^(2)-a^(2))-(a^(2)-b^(2))- ..............

`(b^(2)-a^(2))-(a^(2)-b^(2))-` ........... .

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To solve the expression \((b^2 - a^2) - (a^2 - b^2)\), we can follow these steps: ### Step-by-Step Solution: 1. **Write down the expression**: \[ (b^2 - a^2) - (a^2 - b^2) \] 2. **Apply the difference of squares formula**: The difference of squares formula states that \(x^2 - y^2 = (x - y)(x + y)\). We can apply this to both parts of the expression. - For \(b^2 - a^2\), we can write: \[ b^2 - a^2 = (b - a)(b + a) \] - For \(a^2 - b^2\), we can write: \[ a^2 - b^2 = (a - b)(a + b) = -(b - a)(a + b) \] 3. **Substitute back into the expression**: Now substituting these back into the original expression, we get: \[ (b - a)(b + a) - (-(b - a)(a + b)) \] This simplifies to: \[ (b - a)(b + a) + (b - a)(a + b) \] 4. **Factor out the common term**: Notice that \((b - a)\) is common in both terms: \[ (b - a)((b + a) + (a + b)) \] 5. **Combine like terms**: \[ (b - a)(2b) \] 6. **Final expression**: Thus, the final simplified expression is: \[ 2b(b - a) \] ### Final Answer: \[ 2b(b - a) \]
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