Question 4(iii)
Simplify:
$(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$

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Solution

$(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$
$= (7 m)^{2} - 2 \times 7 m \times 8 n + (8 n)^{2} + [(7 m)^{2} + 2 \times 7 m \times 8 n + (8 n)^{2}]$
$[U s i n g I d e n t i t i e s (a + b)^{2} = a^{2} + 2 a b + b^{2} a n d (a - b)^{2} = a^{2} - 2 a b + b^{2}]$ $= 49 m^{2} - 112 m n + 64 n^{2} + [49 m^{2} + 112 m n + 64 n^{2}]$
$= 98 m^{2} + 128 n^{2}$

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Question 4(iii)
Simplify:
$(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$

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

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

(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) (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

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