Factorize- 4x-2 - 9y-2 - 16z-2 - 12xy - 24yz - 16xz - Maths Q-A

Factorize the given polynomial4x^2+9y^2+16z^2+12xy 24yz 16xz0ex0ex=(2x)^2+(3y)^2+( 4z)^2+2× 2x× 3y+2× 3y× ( 4z)+2× ( 4z)×(2x)Use the identity (a+b+c)^2=a^2+b^2+ ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

Factorize: 4x...

Question

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

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Solution

Factorize the given polynomial
$4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z = {(2 x)}^{2} + {(3 y)}^{2} + {(- 4 z)}^{2} + 2 \times 2 x \times 3 y + 2 \times 3 y \times (- 4 z) + 2 \times (- 4 z) \times (2 x)$
Use the identity ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z = {(2 x + 3 y - 4 z)}^{2}$
Hence the factorized form of the polynomial $4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z$ is $(2 x + 3 y - 4 z)$ $(2 x + 3 y - 4 z)$ .

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Similar questions

Q. Factorize: 4x² + 9y² + 16z² + 12xy − 24yz − 16xz.

Q. Factorise:
(i)

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

(ii)

2 x^{2} + y^{z} + 8 z^{2} - 2 \sqrt{2} x y + 4 \sqrt{2} y z - 8 x z

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

Let

P (x) = 4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y + 24 y z + 16 x z

factorize

P (x)

for

x = 1, y = 1, z = 1.

Q. State True or False.

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

= (2 x + 3 y - 4 z) (2 x + 3 y - 4 z)

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Factorize: 4x2+9y2+16z2+12xy-24yz-16xz.

Factorize the given polynomial4x2+9y2+16z2+12xy-24yz-16xz=(2x)2+(3y)2+(-4z)2+2×2x×3y+2×3y×(-4z)+2×(-4z)×(2x)Use the identity (a+b+c)2=a2+b2+c2+2ab+2bc+2ac4x2+9y2+16z2+12xy-24yz-16xz=(2x+3y-4z)2Hence the factorized form of the polynomial 4x2+9y2+16z2+12xy-24yz-16xz is (2x+3y-4z)(2x+3y-4z).

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