Question

simplify: (p^2-q^2)^3 +(q^2-r^2)^3+(r^2-p^2)^3 divide by (p-q)^3+(q-r)^3+(r-p)^3

Answer 1

IN your question sum of

$(p^{2} - q^{2} ) + (q^{2} - r^{2} ) + (r^{2} -p^{2} ) = 0$

Then their sum of cube will be equal to 3 times these no. such as $(p^{2} - q^{2} )^3 + (q^{2} - r^{2} )^3 + (r^{2} -p^{2} ) ^3 = 3.(p^{2} - q^{2} ).(q^{2} - r^{2} ).(r^{2} -p^{2} )$


similarly 

$(p-q)^3 + (q-r)^3 + (r-p)^3 = 3.(p-q).(q-r).(r-p)$


Thus

(p^{2} - q^{2} )^3 + (q^{2} - r^{2} )^3 + (r^{2} -p^{2} ) ^3 /(p-q)^3 + (q-r)^3 + (r-p)^3  

 =>  3.(p^{2} - q^{2} ).(q^{2} - r^{2} ).(r^{2} -p^{2} ) / 3.(p-q).(q-r).(r-p) 

=> (p-q)(p+q)(q-r)(q+r)(r-p)(r+p) / (p-q)(q-r)(r-p)  

=>  (p+q)(q+r)(r+p) 

hence this is your answer

Answer 2

Answer:

Step-by-step explanation:Area of cross section of river= 2 x 45 = 90 m²

so, water flowing into the sea= area of cross section x rate of flowing water

= 90 x 3000

= 270000 m³

there water flowing per minute= 270000 / 60 = 4500 m³