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\sqrt{7}\sqrt{3}+\sqrt{7}\sqrt{19}-\sqrt{5}\sqrt{3}-\sqrt{5}\sqrt{19}
Apply the distributive property by multiplying each term of \sqrt{7}-\sqrt{5} by each term of \sqrt{3}+\sqrt{19}.
\sqrt{21}+\sqrt{7}\sqrt{19}-\sqrt{5}\sqrt{3}-\sqrt{5}\sqrt{19}
To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.
\sqrt{21}+\sqrt{133}-\sqrt{5}\sqrt{3}-\sqrt{5}\sqrt{19}
To multiply \sqrt{7} and \sqrt{19}, multiply the numbers under the square root.
\sqrt{21}+\sqrt{133}-\sqrt{15}-\sqrt{5}\sqrt{19}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
\sqrt{21}+\sqrt{133}-\sqrt{15}-\sqrt{95}
To multiply \sqrt{5} and \sqrt{19}, multiply the numbers under the square root.