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

May 4, 2016

$- 100$

#### Explanation:

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

$4 \sqrt{7} \left(5 \sqrt{7} + 10 \sqrt{3}\right) - 8 \sqrt{3} \left(5 \sqrt{7} + 10 \sqrt{3}\right)$

Noting that : $\sqrt{a} \times \sqrt{a} = a$

and from the question here $\sqrt{7} \times \sqrt{7} = 7$

distribute 1st bracket

$\Rightarrow \left(4 \sqrt{7} \times 5 \sqrt{7}\right) + \left(4 \sqrt{7} \times 10 \sqrt{3}\right) = 140 + 40 \sqrt{21}$

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

distribute 2nd bracket

$\Rightarrow \left(- 8 \sqrt{3} \times 5 \sqrt{7}\right) + \left(- 8 \sqrt{3} \times 10 \sqrt{3}\right)$

$= - 40 \sqrt{21} - 240$

Combining the 2 expansions

$140 + 40 \sqrt{21} - 40 \sqrt{21} - 240$

[Note : 40sqrt21-40sqrt21=0]

$\Rightarrow \left(4 \sqrt{7} - 8 \sqrt{3}\right) \left(5 \sqrt{7} + 10 \sqrt{3}\right) = 140 - 240 = - 100$