Question

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

Answer 1

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