Question

Factorise (P + q + r)^2 -( P-q - r)^2 + 4q²-4r²​

Answer 1

Step-by-step explanation:

=>(p+q+r)²-(p-q-r)²+4q²-4r²

=>p²+q²+r²+2pq+2qr+2pr-{p²+(-q)²+(-r)²+2p(-q)+2(-q)(-r)+2p(-r)}+4q²-4r²

=>p²+q²+r²+2pq+2qr+2pr-{p²+q²+r²-2pq+2qr-2pr}+4q²-4r²

=>p²+q²+r²+2pq+2qr+2pr-p²-q²-r²+2pq-2qr+2pr+4q²-4r²

=>4pq+4pr+4q²-4r²

=>4p(q+r)+4(q²-r²)

=>4p(q+r)+4(q+r)(q-r)

=>4(q+r){p+q-r}

good luck

Answer 2

Answer:

=>(p+q+r)²-(p-q-r)²+4q²-4r²

=>p²+q²+r²+2pq+2qr+2pr-{p²+(-q)²+(-r)²+2p(-q)+2(-q)(-r)+2p(-r)}+4q²-4r²

=>p²+q²+r²+2pq+2qr+2pr-{p²+q²+r²-2pq+2qr-2pr}+4q²-4r²

=>p²+q²+r²+2pq+2qr+2pr-p²-q²-r²+2pq-2qr+2pr+4q²-4r²

=>4pq+4pr+4q²-4r²

=>4p(q+r)+4(q²-r²)

=>4p(q+r)+4(q+r)(q-r)

=>4(q+r){p+q-r}