Math, asked by buddhapriyapatra, 2 months ago

Verify that (11pq + 4q)^2-(11pq − 4q)^2=176pq^2

Answers

Answered by Syamkumarr
2

Answer:

( 11pq + 4q)^{2} - (11pq - 4q)^{2}  = 176pq^{2} is true

Step-by-step explanation:

take L H S part (11pq + 4q)^{2} - (11pq -4q)^{2}

expand the above equation by using formulas

(a+b)^{2} = a^{2} +b^{2} +2ab  and ( a+b)^{2} = a^{2} + b^{2} -2ab

=(11pq + 4q)^{2} - (11pq -4q)^{2} \\=( 11pq)^{2} +(4q )^{2} + 2 ( 11pq ) (4q) -[ (11pq)^{2} - (4q)^{2}  - 2(11pq ) (4q) ]\\=121 p^{2}q^{2}  + 16 q^{2}  + 88p q^{2} - [ 121 p^{2} q^{2}  +16 q^{2} - 88 p q^{2} ]\\= 121 p^{2} q^{2} +16 q^{2} + 88pq^{2} -121 p^{2} q^{2} -16 q^{2} +88pq^{2}

after subtractions  of 121 p^{2} q^{2} -121p^{2} q^{2} , 16q^{2} -16 q^{2}

            = 88 pq^{2} + 88pq^{2} \\=176 pq^{2}

∴ it is true that ( 11pq + 4q )^{2} - (11pq -4q)^{2} = 176 pq^{2}

Similar questions