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Factorise: (i) 4x^2+9y^2+16z^2+12xy-24yz-16xz (ii) 2x^2+y^z+8z

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Factorise:
(i) $4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 yz - 16 x z$
(ii) $2 x^{2} + y^{z} + 8 z^{2} - 22 x y + 42 yz - 8 x z$

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Factorise:
(i)

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

(ii)

2 x^{2} + y^{z} + 8 z^{2} - 22 x y + 42 yz - 8 x z

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Text solutionVerified

We know that

(x^{2} + y^{2} + z^{2} + 2 x y + 2 yz + z x) = (x + y + z)^{2}

(i)

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

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

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

(ii)

2 x^{2} + y^{2} + 8 z^{2} - 22 x y + 42 yz - 8 z x

= (- 2 x) + (y)^{2} + (2 z) + 2 (- 2 x) (y) + 2 (y) (22 z) + 2 (22 z) (y)

= (- 2 x + y + 22 z)^{2} = (- 2 x + y + 22 z) (- 2 x + y + 22 z)

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Question Text	Factorise: (i) $4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 yz - 16 x z$ (ii) $2 x^{2} + y^{z} + 8 z^{2} - 22 x y + 42 yz - 8 x z$
Answer Type	Text solution:1
Upvotes	150