Factorise: 2x2+y2+8z2-2
Answers
Answer:
Answer: The answer is (-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).(−
2
x+y+2
2
z)(−
2
x+y+2
2
z). )
Step-by-step explanation: We are given to factorise the following expression:
E=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz.E=2x
2
+y
2
+8z
2
−2
2
xy+4
2
yz−8xz.
We will be using the following factorisation formula:
(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca.(a+b+c)
2
=a
2
+b
2
+c
2
+2ab+2bc+2ca.
We have
\begin{gathered}E\\\\=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz\\\\=(-\sqrt2x)^2+y^2+(2\sqrt2z)^2+2(-\sqrt2x)y+2y(2\sqrt2z)+2(2\sqrt2z)(-\sqrt2x)\\\\=(-\sqrt2x+y+2\sqrt2z)^2\\\\=(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).\end{gathered}
E
=2x
2
+y
2
+8z
2
−2
2
xy+4
2
yz−8xz
=(−
2
x)
2
+y
2
+(2
2
z)
2
+2(−
2
x)y+2y(2
2
z)+2(2
2
z)(−
2
x)
=(−
2
x+y+2
2
z)
2
=(−
2
x+y+2
2
z)(−
2
x+y+2
2
z).
Thus, the answer is (-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).(−
2
x+y+2
2
z)(−
2
x+y+2
2
z).