Factors of $25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}$ are

(5 a - 2 b + 7 c)

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1

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(5 a + 2 b - 7 c)

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0

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Solution

The correct options are
A $(5 a - 2 b + 7 c)$
B $1$
D $(5 a + 2 b - 7 c)$
$25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}$
$= (5 a)^{2} - (4 b^{2} - 28 b c + 49 c^{2})$
$= (5 a)^{2} - (2 b)^{2} - 2 \times 2 b \times 7 c + (7 c)^{2}$
$= (5 a)^{2} - (2 b - 7 c)^{2}$
$= (5 a + 2 b - 7 c) (5 a - 2 b + 7 c)$
$= 1 \times (5 a + 2 b - 7 c) \times (5 a - 2 b + 7 c)$

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Similar questions

25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}

25 a^{2} - 4 b^{2} + 5 a + 2 b

25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}

25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}

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$25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}$

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