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Factorise $4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 yz - 16 x z$ .

Class 9Algebraic IdentitiesPolynomials

A $(2 x + 3 y - 4 z)^{2}$
B $(2 x - 3 y + 4 z)^{2}$
C $(2 x + 3 y + 4 z)^{2}$
D $(- 2 x + 3 y + 4 z)^{2}$

Step-by-Step Solution

The squares are

(2 x)^{2}, (3 y)^{2}, (4 z)^{2} . x y

is positive,

yz

and

x z

are negative, so

z

has the opposite sign to

x

and

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

.

Answer: A)

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

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