Expand using identity : $(3 x + 5 y + 2 z) (3 x - 5 y + 2 z)$

16 x^{2} - 12 x z + 4 z^{2} - 25 y^{2}

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9 x^{2} + 12 x z + 4 z^{2} - 25 y^{2}

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22 x^{2} + 12 x z + 4 z^{2} + 25 y^{2}

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13 x^{2} - 12 x z + 4 z^{2} - 25 y^{2}

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Solution

The correct option is C $9 x^{2} + 12 x z + 4 z^{2} - 25 y^{2}$
$(3 x + 5 y + 2 z) (3 x - 5 y + 2 z)$
$= (3 x + 2 z + 5 y) (3 x + 2 z - 5 y)$
$= (3 x + 2 z)^{2} - (5 y)^{2}$ ...[Using $a^{2} - b^{2} = (a + b) (a - b)$ ]
$= ((3 x)^{2} + 2 (3 x) (2 z) + (2 z)^{2}) - 25 y^{2}$ ....[Using $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ]
$= 9 x^{2} + 12 x z + 4 z^{2} - 25 y^{2}$

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Similar questions

Factorize: $9 x^{2} + 16 y^{2} + 4 z^{2} - 24 x y + 16 y z - 12 x z$

p (x) = 9 x^{2} + y^{2} + 4 z^{2} + 6 x y - 4 y z - 12 x z

P (x)

x = 1, y = 1, z = 1

Multiply 9x²+25y²+15xy+12x-20y+16 by 3x-5y-4 using suitable identity

9 x^{2} + 25 y^{2} = 181 a n d x y = - 6

3 x + 5 y = 11

x y = 2

9 x^{2} + 25 y^{2}

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