Question

5. Factorise:
(i) 2x2 + y2 + 8z2 - 272 xy + 412 yz - 8x2​

Answer 1

Answer:

$Answer: The answer is (-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).(−2x+y+22z)(−2x+y+22z). )</p><p></p><p>Step-by-step explanation:  We are given to factorise the following expression:</p><p></p><p>E=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz.E=2x2+y2+8z2−22xy+42yz−8xz.</p><p></p><p>We will be using the following factorisation formula:</p><p></p><p>(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca.(a+b+c)2=a2+b2+c2+2ab+2bc+2ca.</p><p></p><p>We have</p><p></p><p>\begin{gathered}E\\\\=2x^2+y^2+8z^2-2\sqrt2xy+4\sqrt 2yz-8xz\\\\=(-\sqrt2x)^2+y^2+(2\sqrt2z)^2+2(-\sqrt2x)y+2y(2\sqrt2z)+2(2\sqrt2z)(-\sqrt2x)\\\\=(-\sqrt2x+y+2\sqrt2z)^2\\\\=(-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).\end{gathered}E=2x2+y2+8z2−22xy+42yz−8xz=(−2x)2+y2+(22z)2+2(−2x)y+2y(22z)+2(22z)(−2x)=(−2x+y+22z)2=(−2x+y+22z)(−2x+y+22z).</p><p></p><p>Thus, the answer is (-\sqrt2x+y+2\sqrt2z)(-\sqrt2x+y+2\sqrt2z).(−2x+y+22z)(−2x+y+22z).</p><p></p><p>$

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Answer 2

Answer:

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