Let us exand the given epxression: (7m 3n 4k)^2=(7m)^2+( 3n)^2+( 4k)^2=[2× (7m)× ( 3n)]+[2× ( 3n)× ( 4k)]+[2× (7m)× ( 4k)] By using the formula, (a+b+c)^2=a^2+b ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (x+y+z)^2

Expand: 7m-3n...

Question

Expand: $(7 m - 3 n - 4 k)^{2}$

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Solution

Let us exand the given epxression:
$(7 m - 3 n - 4 k)^{2} = (7 m)^{2} + (- 3 n)^{2} + (- 4 k)^{2} = [2 \times (7 m) \times (- 3 n)] + [2 \times (- 3 n) \times (- 4 k)] + [2 \times (7 m) \times (- 4 k)]$
By using the formula,
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
Here, $a = 7 m, b = - 3 n, c = - 4 k$
Now, substitute the value we get
$= 49 m^{2} + 9 n^{2} + 16 k^{2} + [- 42 m n] + [24 n k] + [- 56 m k]$
$= 49 m^{2} + 9 n^{2} + 16 k^{2} - 42 m n + 24 n k - 56 m k$
$∴ (7 m - 3 n - 4 k)^{2} = 49 m^{2} + 9 n^{2} + 16 k^{2} - 42 m n + 24 n k - 56 m k$

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Expand: (7m−3n−4k)2

Expand: $(7 m - 3 n - 4 k)^{2}$