Question

5. Factorise

$\huge\fbox{\color{Green,Red}{Question}}$

2x² + y² +8z² - 2√2 xy + 4√2 yz - 8xz​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

${\star{\sf{\green{ \: 2 {x}^{2} + {y}^{2} + 8 {z}^{2} - 2 \sqrt{2}xy + 4 \sqrt{2} yz - 8xz}}}}$

• From perfect square we can't find that which term has(+) sign or (-) sign.
• From next term we can find that the terms which has negative sign and in these terms which number is repeating.
• Therefore we will put negative sign to this term.

${\bf{\blue{\underline{Now:}}}}$

${\implies{\sf{2 {x + {y}^{2} + 8z - 2 \sqrt{2} xy + 4 \sqrt{2} yz-8xz}}}}$

${\implies{\sf{( - \sqrt{2}) + ( {y)}^{2} + (2 \sqrt{2})^{2} -( 2 \times \sqrt{2x} \times y )+( 2 \times y \times 2 \sqrt{2z} ) - (2 \times 2 \sqrt{2} z \times \sqrt{2x} )}}}$

${\implies{\sf{ \big( - \sqrt{2x } + y + 2 \sqrt{2}z \big) ^{2} }}}$

${\implies{\sf{ \big( - \sqrt{2x } + y + 2 \sqrt{2}z \big) \big( - \sqrt{2} x + y + 2 \sqrt{2} z \big) }}}$