Simplify:
$(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ .

198 m^{2} + 28 n^{2}

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

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98 m + 128 n

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98 m^{2} - 128 n^{2}

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Solution

The correct option is B $98 m^{2} + 128 n^{2}$
Given, $(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ .

We know, $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
and $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ .

Then,
$(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$
$= [(7 m)^{2} - 2 (7 m) (8 n) + (8 n)^{2}] + [(7 m)^{2} + 2 (7 m) (8 n) + (8 n)^{2}]$
$= (49 m^{2} - 112 m n + 64 n^{2}) + (49 m^{2} + 112 m n + 64 n^{2})$
$= 49 m^{2} - 112 m n + 64 n^{2} + 49 m^{2} + 112 m n + 64 n^{2}$
$= 98 m^{2} + 128 n^{2}$ .

Therefore, option $B$ is correct.

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Similar questions

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}}

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

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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Simplify:(7m−8n)2+(7m+8n)2.

Simplify:
$(7 m - 8 n)^{2} + (7 m + 8 n)^{2}$ .