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Question

Simplify:

(1) (l + m + n)2 + (l – m + n)2
(2) (2x + y + z)2 – (2x + y – z)2
(3) (p + 3q + r)2 – (p – 3q + r)2
(4) (7a – 6b – 5c)2 + (7a + 6b – 5c)2

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Solution

(1) (l + m + n)2 + (l – m + n)2
=l2+m2+n2+2lm+2mn+2nl+l2+m2+n2-2lm-2mn+2nl=2l2+2n2+2m2+4nl

(2)(2x + y + z)2 – (2x + y – z)2
=4x2+y2+z2+4xy+2yz+4xz -4x2+y2+z2+4xy-2yz-4xz=4x2+y2+z2+4xy+2yz+4xz-4x2-y2-z2-4xy + 2yz + 4xz=4yz+8xz

(3) (p + 3q + r)2 – (p – 3q + r)2
=p2+9q2+r2+6pq+6qr+2rp-p2+9q2+r2-6pq-6qr+2rp=p2+9q2+r2+6pq+6qr+2rp-p2-9q2-r2+6pq+6qr-2rp=12pq+12qr

(4) (7a – 6b – 5c)2 + (7a + 6b – 5c)2
=49a2+36b2+25c2-84ab+60bc-70ca+49a2+36b2+25c2+84ab-60bc-70ca=98a2+72b2+50c2-140ca

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