Question

Question5. Factories:
(1)
$4 { }^{2} + 9y {}^{2} +16z {}^{2} + 12xy - 24yz - 16xz$
(2)
$2x {}^{2} + y {}^{2} + 8z {}^{2} - 2 \sqrt{2} \: xy + 4 \sqrt{2} \: yz - 8xz$
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Answer 1

Answer:

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

Top answer · 72 votes

We know that (x^2 + y^2 + z^2 + 2xy + 2yz + zx) = (x + y + z)^2 (i) 4x^2 + 9y^2 + 16z^2 + 12xy - 24yz - 16xz = (2x)^2 + (3y)^2 + ( - 4z)^2 + 2(2x)(3y)

Answer 2

Answer:

$\huge\fbox \red{ANS} {\colorbox{crimson}{W}}\fbox\red{ER}$

Step-by-step explanation:

◆4x²+ 9y² + 16z² + 12xy - 24yz - 16xz 2²x2 +

3y²+4² z² + 12xy - 24yz - 16xz

↣ ( 2x )² + ( 3y )²+ ( 4z )²+ 12xy - 24yz - 16xz

↣ ( 2x )²+ ( 3y )² + ( -4z )²+ 12xy – 24yz - 16xz

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

↣ ( -4z) + 2 ( 2x ) ( -4z)

Using ( a + b + c )²= a² + b² + c² + 2ab + 2bc + 2ac

Putting a = 2x , b = 3y , c = -4z

↣ ( 2x + 3y - 4z )²

➸ ( 2x + 3y - 4z ) ( 2x + 3y - 4z )

Hope it's helpful↑(◍•ᴗ•◍)❤࿐