## College Algebra 7th Edition

We start with the left side: $(a^{2}+b^{2})(c^{2}+d^{2})=a^{2}c^{2}+a^{2}d^{2}+b^{2}c^{2}+b^{2}d^{2} =(a^{2}c^{2}+b^{2}d^{2}+2abcd)+(a^{2}d^{2}+b^{2}c^{2}-2abcd)=(ac+bd)^{2}+(ad-bc)^{2}$ Which equals the right side.