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Question

Simplify and find the value of the algebric expression if m=5 and n=10.

(i) (m2n2m)2+2m3n2

(ii) (7m8n)2+(7m+8n)2

(iii) (m2n2)2 [3 MARKS]

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Solution

Application: 1 Mark each

Using the identity :
(a+b)2=a2+2ab+b2

(i)(m2n2m)2+2m3n2

=(m2)2+(n2m)22(m2)(n2m)+2m3n2

=m4+n4m22(m)3n2+2m3n2

=m4+n4m2

=(5)4+(10)4(5)2

=625+250000

=250625


(ii) (7m8n)2+(7m+8n)2

=(7m)2+(8n)22(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) (m2n2)2

=((m)2)2+(n2)22(m)2(n)2

=m4+n42m2n2

=(5)4+(10)42(5)2(10)2

=625+100005000

=5625


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