1.

Factorise 9x^2 + 4y^2 + 16z^2 + 12xy - 16yz -24xz

Answer»

Answer:

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

Step-by-step explanation:

GIVEN an ALGEBRAIC expressionsuch that,

9 {x}^{2} + 4 {y}^{2} + 16 {z}^{2} + 12xy - 16yz - 24xz

To factorise it.

Further simplifying, we can write it as,

= {(3x)}^{2} + {(2y)}^{2} + {( - 4z)}^{2} + 2(3x)(2y) + 2(2y)( - 4z) + 2(3x)( - 4z)

But, we KNOW that,

{a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ac = {(a + b + c)}^{2}

Therefore, we will GET,

= {((3x) +( 2y )+ ( - 4z))}^{2} \\ \\ = {(3x + 2y - 4z)}^{2}

Hence, the required VALUE is (3x+2y-4z)(3x+2y-4z).

Some more identities :-

  • {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}
  • {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}
  • (x + y)(x - y) = {x}^{2} - {y}^{2}


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