Factorise: 4x²+9y²+16z²+12xy-24yz-16xz
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Answered by
296
Solution:
4x²+9y²+16z²+12xy -24yz -16xz
= (2x)²+(3y)²+(4z)²+2(2)(3)xy -2(3)(4)yz -2(2x)(4z)
= (2x + 3y - 4z)(2x + 3y - 4z)
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Answered by
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Answer:
4x² + 9y² + 16z² + 12xy - 24yz - 16xz can be factorized as
(2x + 3y - 4z)(2x + 3y - 4z)
Step-by-step explanation:
Given equation : 4x²+9y²+16z²+12xy-24yz-16xz
This can be written as
= (2x)²+(3y)²+2*(2x)*(3y)+(4z)²-2*(3y)*(4z)-2*(2x)*(4z)
We know that (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Comparing both the equations, we get,
a = 2x , b = 3y , c = - 4z
Therefore,
=> (2x)²+(3y)²+2*(2x)*(3y)+(4z)²-2*(3y)*(4z)-2*(2x)*(4z)
= (2x + 3y - 4z)²
= (2x + 3y - 4z)(2x + 3y - 4z)
Therefore, 4x²+9y²+16z²+12xy-24yz-16xz can be factorized as
(2x + 3y - 4z)(2x + 3y - 4z)
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