Write the following in the expanded form
$(3 x - 2 y + 5 z)^{2}$

9 x^{2} + 4 y^{2} + 25 z^{2} + 12 x y + 20 y z + 30 z x

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9 x^{2} + 4 y^{2} + 25 z^{2} - 12 x y - 20 y z + 30 z x

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9 x^{2} + 4 y^{2} + 25 z^{2} - 6 x y - 10 y z + 15 z x

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9 x^{2} + 4 y^{2} + 25 z^{2} - 24 x y - 40 y z + 60 z x

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Solution

The correct option is D $9 x^{2} + 4 y^{2} + 25 z^{2} - 12 x y - 20 y z + 30 z x$
We solve the given expression $(3 x - 2 y + 5 z)^{2}$ as shown below:

$(3 x - 2 y + 5 z)^{2}$

$= (3 x)^{2} + (- 2 y)^{2} + (5 z)^{2} + (2 \times 3 x \times (- 2 y)) + (2 \times (- 2 y) \times 5 z) + (2 \times 5 z \times 3 x)$

$(∵ (a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a)$

$= 9 x^{2} + 4 y^{2} + 25 z^{2} - 12 x y - 20 y z + 30 z x$

Hence, $(3 x - 2 y + 5 z)^{2} = 9 x^{2} + 4 y^{2} + 25 z^{2} - 12 x y - 20 y z + 30 z x$ .

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Similar questions

Q. State whether the statement is True or False.

Expand:

(3 x - 4 y + 5 z)^{2}

is equal to

9 x^{2} + 16 y^{2} + 25 z^{2} - 24 x y - 24 x y - 40 y z + 30 z x

Find the following products:

(i) (3x + 2y + 2z) (9x² + 4y² + 4z² − 6xy − 4yz − 6zx)

(ii) (4x − 3y + 2z) (16x² + 9y² + 4z² + 12xy + 6yz − 8zx)

(iii) (2ab − 3b − 2c) (4a² + 9b² +4c² + 6 ab − 6 bc + 4ca)

(iv) (3x − 4y + 5z) (9x² +16y²+ 25z² + 12xy −15zx + 20yz)

Q. If

x, y, z

are real and

9 x^{2} + 16 y^{2} + 25 z^{2} - 12 x y - 20 y z - 15 z x = 0,

then

x, y, z

are in

Factorise :

$(3 x - 4 y)^{2} - 25 z^{2}$

Q. Factorise:

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

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Write the following in the expanded form(3x−2y+5z)2

Write the following in the expanded form
$(3 x - 2 y + 5 z)^{2}$