Question

x2 + 4y2 + 9z2 - 4xy + 12yz - 6zx​

Answer 1

Answer:

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Answer 2

Answer:

\red{x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zx}x

2

+4y

2

+9z

2

−4xy+12yz−6zx

\green{=(-x+2y+3z)(-x+2y+3z)}=(−x+2y+3z)(−x+2y+3z)

Step-by-step explanation:

Given \: x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zxGivenx

2

+4y

2

+9z

2

−4xy+12yz−6zx

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

2

+(2y)

2

+(3z)

2

+2×(−x)×2y+2×2y×3z+2×3z×(−x)

= (-x+2y+3z)^{2}=(−x+2y+3z)

2

\boxed {\pink { Since,\:a^{2}+b^{2}+c^{2}+2ab+2bc+2ca = (a+b+c)^{2}}}

Since,a

2

+b

2

+c

2

+2ab+2bc+2ca=(a+b+c)

2

Therefore.,

\red{x^{2}+4y^{2}+9z^{2}-4xy+12yz-6zx}x

2

+4y

2

+9z

2

−4xy+12yz−6zx

\green{=(-x+2y+3z)(-x+2y+3z)}=(−x+2y+3z)(−x+2y+3z)

hope it is helpful to you

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