Question

How do you simplify `(4sqrt7-8sqrt3)(5sqrt7+10sqrt3)`?

Answer 1

`-100`

Explanation:

Expand the brackets using FOIL or multiply each term in the 2nd bracket by each term in the 1st.

`4sqrt7(5sqrt7+10sqrt3)-8sqrt3(5sqrt7+10sqrt3)`

Noting that : `sqrtaxxsqrta=a`

and from the question here `sqrt7xxsqrt7=7`

distribute 1st bracket

`rArr(4sqrt7xx5sqrt7)+(4sqrt7xx10sqrt3)=140+40sqrt21`

`[" using " sqrtaxxsqrtbhArrsqrtab]"so"sqrt7xxsqrt3=sqrt21`

distribute 2nd bracket

`rArr(-8sqrt3xx5sqrt7)+(-8sqrt3xx10sqrt3)`

`=-40sqrt21-240`

Combining the 2 expansions

`140+40sqrt21-40sqrt21-240`

[Note : `40sqrt21-40sqrt21=0]`

`rArr(4sqrt7-8sqrt3)(5sqrt7+10sqrt3)=140-240=-100`