Simplify and find the value of the algebric expression if m=5 and n=10.
(i) (m2−n2m)2+2m3n2
(ii) (7m−8n)2+(7m+8n)2
(iii) (m2−n2)2 [3 MARKS]
Application: 1 Mark each
Using the identity :
(a+b)2=a2+2ab+b2
(i)(m2−n2m)2+2m3n2
=(m2)2+(n2m)2−2(m2)(n2m)+2m3n2
=m4+n4m2−2(m)3n2+2m3n2
=m4+n4m2
=(5)4+(10)4(5)2
=625+250000
=250625
(ii) (7m−8n)2+(7m+8n)2
=(7m)2+(8n)2−2(7m)(8n)+(7m)2+(8n)2+2(7m)(8n)
=49m2+64n2+49m2+64n2
=98m2+128n2
=98(5)2+128(10)2
=2450+12800
=15250
(iii) (m2−n2)2
=((m)2)2+(n2)2−2(m)2(n)2
=m4+n4−2m2n2
=(5)4+(10)4−2(5)2(10)2
=625+10000−5000
=5625