{a²+b²/2}²+{a²-b²/2}²

1Find common denominator\(\left( a^{2}+\frac{b^{2}}{2}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\left( \frac{\textcolor{#B14BA5}{2}}{\textcolor{#B14BA5}{2}}a^{2}+\frac{b^{2}}{2}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)2Combine multiplied terms into a single fraction\(\left( \frac{2}{2}a^{2}+\frac{b^{2}}{2}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\left( \frac{2a^{2}}{2}+\frac{b^{2}}{2}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)3Combine fractions with common denominator\(\left( \frac{2a^{2}}{\textcolor{#B14BA5}{2}}+\frac{b^{2}}{\textcolor{#B14BA5}{2}}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\left( \frac{2a^{2}+b^{2}}{\textcolor{#B14BA5}{2}}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)4Distribute exponent\(\left( \frac{2a^{2}+b^{2}}{2}\right) ^{2}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{2^{2}}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)5Evaluate the exponent\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{\textcolor{#B14BA5}{2^{2}}}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{\textcolor{#B14BA5}{4}}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)6Find common denominator\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( \frac{\textcolor{#B14BA5}{2}}{\textcolor{#B14BA5}{2}}a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)7Combine multiplied terms into a single fraction\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( \frac{2}{2}a^{2}+\frac{-b^{2}}{2}\right) ^{2}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( \frac{2a^{2}}{2}+\frac{-b^{2}}{2}\right) ^{2}\)8Combine fractions with common denominator\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( \frac{2a^{2}}{\textcolor{#B14BA5}{2}}+\frac{-b^{2}}{\textcolor{#B14BA5}{2}}\right) ^{2}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( \frac{2a^{2}-b^{2}}{\textcolor{#B14BA5}{2}}\right) ^{2}\)9Distribute exponent\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\left( \frac{2a^{2}-b^{2}}{2}\right) ^{2}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\frac{\left( 2a^{2}-b^{2}\right) ^{2}}{2^{2}}\)10Evaluate the exponent\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\frac{\left( 2a^{2}-b^{2}\right) ^{2}}{\textcolor{#B14BA5}{2^{2}}}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{4}+\frac{\left( 2a^{2}-b^{2}\right) ^{2}}{\textcolor{#B14BA5}{4}}\)11Combine fractions with common denominator\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}}{\textcolor{#B14BA5}{4}}+\frac{\left( 2a^{2}-b^{2}\right) ^{2}}{\textcolor{#B14BA5}{4}}\)\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}+\left( 2a^{2}-b^{2}\right) ^{2}}{\textcolor{#B14BA5}{4}}\)12Expand the square\(\frac{\left( 2a^{2}+b^{2}\right) ^{2}+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)\(\frac{\left( 2a^{2}+b^{2}\right) \left( 2a^{2}+b^{2}\right) +\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)13Distribute\(\frac{\textcolor{#B14BA5}{\left( 2a^{2}+b^{2}\right) \left( 2a^{2}+b^{2}\right) }+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)\(\frac{\textcolor{#B14BA5}{2a^{2}\left( 2a^{2}+b^{2}\right) +b^{2}\left( 2a^{2}+b^{2}\right) }+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)14Distribute\(\frac{\textcolor{#B14BA5}{2a^{2}\left( 2a^{2}+b^{2}\right) }+b^{2}\left( 2a^{2}+b^{2}\right) +\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)\(\frac{\textcolor{#B14BA5}{4a^{4}+2a^{2}b^{2}}+b^{2}\left( 2a^{2}+b^{2}\right) +\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)15Distribute\(\frac{4a^{4}+2a^{2}b^{2}+\textcolor{#B14BA5}{b^{2}\left( 2a^{2}+b^{2}\right) }+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)\(\frac{4a^{4}+2a^{2}b^{2}+\textcolor{#B14BA5}{2a^{2}b^{2}+b^{4}}+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)16Combine like terms\(\frac{4a^{4}+\textcolor{#B14BA5}{2a^{2}b^{2}}+\textcolor{#B14BA5}{2a^{2}b^{2}}+b^{4}+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)\(\frac{4a^{4}+\textcolor{#B14BA5}{4a^{2}b^{2}}+b^{4}+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)17Expand the square\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+\left( 2a^{2}-b^{2}\right) ^{2}}{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+\left( 2a^{2}-b^{2}\right) \left( 2a^{2}-b^{2}\right) }{4}\)18Distribute\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+\textcolor{#B14BA5}{\left( 2a^{2}-b^{2}\right) \left( 2a^{2}-b^{2}\right) }}{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+\textcolor{#B14BA5}{2a^{2}\left( 2a^{2}-b^{2}\right) -b^{2}\left( 2a^{2}-b^{2}\right) }}{4}\)19Distribute\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+\textcolor{#B14BA5}{2a^{2}\left( 2a^{2}-b^{2}\right) }-b^{2}\left( 2a^{2}-b^{2}\right) }{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+\textcolor{#B14BA5}{4a^{4}-2a^{2}b^{2}}-b^{2}\left( 2a^{2}-b^{2}\right) }{4}\)20Distribute\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}-2a^{2}b^{2}-\textcolor{#B14BA5}{b^{2}\left( 2a^{2}-b^{2}\right) }}{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}-2a^{2}b^{2}-\left( \textcolor{#B14BA5}{2a^{2}b^{2}-b^{2}b^{2}}\right) }{4}\)21Combine exponents\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}-2a^{2}b^{2}-\left( 2a^{2}b^{2}-\textcolor{#B14BA5}{b^{2}b^{2}}\right) }{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}-2a^{2}b^{2}-\left( 2a^{2}b^{2}-\textcolor{#B14BA5}{b^{4}}\right) }{4}\)22Distribute\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}-2a^{2}b^{2}-\left( 2a^{2}b^{2}-b^{4}\right) }{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}-2a^{2}b^{2}-2a^{2}b^{2}+b^{4}}{4}\)23Combine like terms\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}\textcolor{#B14BA5}{-2a^{2}b^{2}}\textcolor{#B14BA5}{-2a^{2}b^{2}}+b^{4}}{4}\)\(\frac{4a^{4}+4a^{2}b^{2}+b^{4}+4a^{4}\textcolor{#B14BA5}{-4a^{2}b^{2}}+b^{4}}{4}\)24Combine like terms\(\frac{\textcolor{#B14BA5}{4a^{4}}+4a^{2}b^{2}+b^{4}+\textcolor{#B14BA5}{4a^{4}}-4a^{2}b^{2}+b^{4}}{4}\)\(\frac{\textcolor{#B14BA5}{8a^{4}}+4a^{2}b^{2}+b^{4}-4a^{2}b^{2}+b^{4}}{4}\)25Combine like terms\(\frac{8a^{4}+\textcolor{#B14BA5}{4a^{2}b^{2}}+b^{4}\textcolor{#B14BA5}{-4a^{2}b^{2}}+b^{4}}{4}\)\(\frac{8a^{4}+\textcolor{#B14BA5}{b^{4}}+b^{4}}{4}\)26Combine like terms\(\frac{8a^{4}+\textcolor{#B14BA5}{b^{4}}+\textcolor{#B14BA5}{b^{4}}}{4}\)\(\frac{8a^{4}+\textcolor{#B14BA5}{2b^{4}}}{4}\)27Cancel terms that are in both the numerator and denominator\(\frac{\textcolor{#B14BA5}{8}a^{4}+\textcolor{#B14BA5}{2}b^{4}}{\textcolor{#B14BA5}{4}}\)Factor the numerator and denominator\(\frac{8a^{4}+2b^{4}}{4}\)\(\frac{2\left( 4a^{4}+b^{4}\right) }{2\cdot 2}\)Cancel multiplied terms that are in the denominator\(\frac{\cancel{2}\left( 4a^{4}+b^{4}\right) }{\cancel{2}\cdot 2}\)\(\frac{4a^{4}+b^{4}}{2}\)\(\frac{\textcolor{#B14BA5}{4}a^{4}+\textcolor{#B14BA5}{b}^{4}}{\textcolor{#B14BA5}{2}}\)24 more stepsShow less Solution \(\frac{4a^{4}+b^{4}}{2}\)