## College Algebra 7th Edition

(a) We start with the right side: $\displaystyle \frac{1}{2}[(a+b)^{2}-(a^{2}+b^{2})]=\frac{1}{2}[(a^{2}+b^{2}+2ab)-a^{2}+b^{2}]=\frac{1}{2}(2ab)=ab$ Which equals the left side. (b) We start with the left side: $(a^{2}+b^{2})^{2}-(a^{2}-b^{2})^{2}=(a^{2})^{2}+(b^{2})^{2}+2a^{2}b^{2}-[(a^{2})^{2}+(b^{2})^{2}-2a^{2}b^{2}]=4a^{2}b^{2}$ Which equals the right side.