Calculate the product: 7sqrt(6)(2sqrt(10)-5sqrt(2))

$$(7 \times 5)\sqrt{6 \times 2} = 35\sqrt{12}$$

So the expression becomes:

$$14\sqrt{60} - 35\sqrt{12}$$

For $\sqrt{60}$:

$$\sqrt{60} = \sqrt{4 \times 15} = \sqrt{4} \times \sqrt{15} = 2\sqrt{15}$$

For $\sqrt{12}$:

$$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$$

$$14(2\sqrt{15}) - 35(2\sqrt{3})$$ $$28\sqrt{15} - 70\sqrt{3}$$

The terms $28\sqrt{15}$ and $70\sqrt{3}$ are not like terms because their radical parts are different, so they cannot be combined further.

The simplified product is $28\sqrt{15} - 70\sqrt{3}$.