Question

216 Factorize using suitable identity :
4x2 + 3 y2 +z2 – 4V3xy – 273yz + 4xz
​

Answer 1

We have,

• To factorise : $\small \rm {4x}^{2} + {3y}^{2} + {z}^{2} - 4 \sqrt{3} xy - 2 \sqrt{3} yz + 4xz$

If,

• An expression is in form of $\small \rm {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac$ , then, it can be factorised as $\small \rm {(a + b + c)}^{2}$

Therefore,

$\to \small\rm {4x}^{2} + {3y}^{2} + {z}^{2} - 4 \sqrt{3} xy - 2 \sqrt{3} yz + 4xz \\ \to \small \rm {(2x)}^{2} + { \big( \sqrt{3}y \big)}^{2} + {(z)}^{2} + 2 \big( - 2 \sqrt{3} xy - \sqrt{3}yz + 2xz \big) \\ \to \large \rm {(2x - \sqrt{3} y +z )}^{2}$

Hence,

• Obtained Factorised terms are (2z - √3y + z)(2z - √3y + z)