How do you simplify (4sqrt7-8sqrt3)(5sqrt7+10sqrt3)(4√7−8√3)(5√7+10√3)?
1 Answer
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)4√7(5√7+10√3)−8√3(5√7+10√3) Noting that :
sqrtaxxsqrta=a√a×√a=a and from the question here
sqrt7xxsqrt7=7√7×√7=7 distribute 1st bracket
rArr(4sqrt7xx5sqrt7)+(4sqrt7xx10sqrt3)=140+40sqrt21⇒(4√7×5√7)+(4√7×10√3)=140+40√21
[" using " sqrtaxxsqrtbhArrsqrtab]"so"sqrt7xxsqrt3=sqrt21[ using √a×√b⇔√ab]so√7×√3=√21 distribute 2nd bracket
rArr(-8sqrt3xx5sqrt7)+(-8sqrt3xx10sqrt3)⇒(−8√3×5√7)+(−8√3×10√3)
=-40sqrt21-240=−40√21−240 Combining the 2 expansions
140+40sqrt21-40sqrt21-240140+40√21−40√21−240 [Note :
40sqrt21-40sqrt21=0]40√21−40√21=0]
rArr(4sqrt7-8sqrt3)(5sqrt7+10sqrt3)=140-240=-100⇒(4√7−8√3)(5√7+10√3)=140−240=−100
