Answer:
solving the expression [tex]\left(2\sqrt{3}-5\sqrt{7}\right)\:\left(2\sqrt{3}-5\sqrt{7}\right)[/tex] we get [tex]\mathbf{187+20\sqrt{21}}[/tex]
Step-by-step explanation:
We need to solve: [tex]\left(2\sqrt{3}-5\sqrt{7}\right)\:\left(2\sqrt{3}-5\sqrt{7}\right)[/tex]
We can write it as:
[tex]\left(2\sqrt{3}-5\sqrt{7}\right)\:\left(2\sqrt{3}-5\sqrt{7}\right)\\=\left(2\sqrt{3}-5\sqrt{7}\right)^2[/tex]
We can use formula: [tex]a^2-b^2=a^2-2ab+b^2[/tex]
[tex]=\left(2\sqrt{3})^2-2(2\sqrt{3})(-5\sqrt{7})+(-5\sqrt{7}\right)^2\\=4(3)+20\sqrt{3}\sqrt{7}+25(7)\\=12+20\sqrt{3\times 7}+175\\=187+20\sqrt{21}[/tex]
So, solving the expression [tex]\left(2\sqrt{3}-5\sqrt{7}\right)\:\left(2\sqrt{3}-5\sqrt{7}\right)[/tex] we get [tex]\mathbf{187+20\sqrt{21}}[/tex]
