Question

Factorize the following

(i) 9x2 +4y2 + 16z2 +12xy-16yz -24xz

(ii) 25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz

iii) 16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz​

Answer 1

ANSWER:

Formula Required:

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

Explanation:

$9 {x}^{2} + {4y}^{2} + 16 {z}^{2} + 12xy + 16yz + 20xz \\ = {( - 3x)}^{2} + {( - 2y)}^{2} + {(4z)}^{2} + 2( - 3x)( - 2y) + 2( - 2y)(4z) + 2( - 3x)(4z) \\ = ( - 3x - 2y + 4z)^{2}$