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

1 Answer
May 4, 2016

Answer:

#-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#