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

$(i) {(m^{2} - n^{2} m)}^{2} + 2 m^{3} n^{2}$

$(i i) {(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$

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Solution

Using the identity :
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

$(i) {(m^{2} - n^{2} m)}^{2} + 2 m^{3} n^{2}$

$= {{(m}^{2})}^{2} + (n^{2} m)^{2} - 2 (m^{2}) (n^{2} m) + 2 m^{3} n^{2}$

$= m^{4} + n^{4} m^{2} - 2 {(m)}^{3} n^{2} + 2 m^{3} n^{2}$

$= m^{4} + n^{4} m^{2}$

$= {(5)}^{4} + {(10)}^{4} {(5)}^{2}$

$= 625 + 250000$

$= 250625$

$(i i) {(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$

$= {(7 m)}^{2} + {(8 n)}^{2} - 2 (7 m) (8 n) + {(7 m)}^{2} + {(8 n)}^{2} + 2 (7 m) (8 n)$

$= 49 m^{2} + 64 n^{2} + 49 m^{2} + 64 n^{2}$

$= 98 m^{2} + 128 n^{2}$

$= 98 {(5)}^{2} + 128 {(10)}^{2}$

$= 2450 + 12800$

$= 15250$

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

(i) {(m^{2} - n^{2} m)}^{2} + 2 m^{3} n^{2}

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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

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

$(i) {(m^{2} - n^{2} m)}^{2} + 2 m^{3} n^{2}$

$(i i) {(7 m - 8 n)}^{2} + {(7 m + 8 n)}^{2}$