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

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

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

$(i i i) {(m^{2} - n^{2})}^{2}$ [3 MARKS]

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Solution

Application: 1 Mark each

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

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

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

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

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

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

$= 625 + 250000$

$= 250625$

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

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

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

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

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

$= 2450 + 12800$

$= 15250$

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

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

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

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

$= 625 + 10000 - 5000$

$= 5625$

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Similar questions

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

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

Simplify:

$(i) (x - y) (x + y) (x^{2} + y^{2}) (x^{4} + y^{4})$ $(i i) (2 x - 1) (2 x + 1) (4 x^{2} + 1) (16 x^{4} + 1)$

$(i i i) (7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ $(i v) (2.5 p - 1.5 q)^{2} - (1.5 p - 2.5 q)^{2}$

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

Simplify.

(i) (a² − b²)²(ii) (2x +5)² − (2x − 5)²

(iii) (7m − 8n)² + (7m + 8n)² (iv) (4m + 5n)² + (5m + 4n)²

(v) (2.5p − 1.5q)² − (1.5p − 2.5q)²

(vi) (ab + bc)² − 2ab²c (vii) (m² − n²m)² + 2m³n²

\frac{(7 m - 8 n)^{2} (7 m + 8 n)^{2}}{(7 m)^{2} - (8 n)^{2}}

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

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