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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Similar questions

Q. Simplify:

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

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

Q. Simplify the expression:

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

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}

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

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

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

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

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

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Algebraic Identities

Standard VIII Mathematics

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Question 4(iii) Simplify: (7m−8n)2+(7m+8n)2

(7m−8n)2+(7m+8n)2 =(7m)2−2×7m×8n+(8n)2+[(7m)2+2×7m×8n+(8n)2] [Using Identities (a+b)2=a2+2ab+b2and (a−b)2=a2−2ab+b2] =49m2−112mn+64n2+[49m2+112mn+64n2] =98m2+128n2

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