Question

Factorize :
(p+2q)3 - (p-2q)3

Answer 1

hey uR AnSwER

(p+2q)3-(p-2q)3

=(3p+6q)-(3p-6q)

Answer 2

Answer:

$\large (p+2q)^3-(p-2q)^3=[(4pq)(3p^2-2q^2)]$

Step-by-step explanation:

$\large \text{we have to factorise (p+2q)^3-(p-2q)^3 }\\\\\\\large \text{using identity}\\\\\\\large (a)^3-(b)^3=(a-b)(a^2+b^2+ab)\\\\\large (p+2q)^3-(p-2q)^3=[(p+2q)-(p-2q)[(p+2q)^2+(p-2q)^2+(p-2q)(p+2q)]] }\\\\\\\large Now \ using \ identity \ (a+b)^2=a^2+b^2+2ab \ and \ (a-b)^2=a^2+b^2-2ab\\\\\\\large (p+2q)^3-(p-2q)^3=[(4q)[(p^2+q^2+4pq+p^2+q^2-4pq+(p-2q)(p+2q)]]\\\\\\\large (p+2q)^3-(p-2q)^3=[(4pq)(2p^2+2q^2+(p-2q)(p+2q)$

$\large \text{Now using identity (a^2-b^2)=(a+b)(a-b) }\\\\\\\large (p+2q)^3-(p-2q)^3=[(4pq)(2p^2+2q^2+p^2-4q^2)]]\\\\\large (p+2q)^3-(p-2q)^3=[(4pq)(3p^2-2q^2)]\\\\\\\large \text{Thus we get our answer} [(4pq)(3p^2-2q^2)]$