[tex]\\ \text{Consider the expression}\\ \\ 2pq+2pr+q^2-r^2\\ \\ \text{to factorize it, we factor out 2p in first two terms and use the difference}\\ \text{of squares formua, }a^2-b^2=(a+b)(a-b)\text{ in last two terms. so we get}\\ \\ 2pq+2pr+q^2-r^2\\ \\ =2p(q+r)+(q+r)(q-r)\\ \\ \text{now factor out (q+r) from both terms to get}\\ \\ =(q+r)[2p+(q-r)]\\ \\ =(q+r)(2p+q-r)[/tex]
Hence the complete factorization is (q+r)(2p+q-r)
