{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 $\frac{4a^{4}+b^{4}}{2}$