Question

factorise 4 x square + 9 y square + 16 z square + 12 x y - 24 Y Z - 16 X Z

Answer 1

$\textbf{Given:}$

$4\,x^2+9\,y^2+16\,z^2+12\,xy-24yz-16xz$

$\textbf{To find:}$

$\text{Factors of 4\,x^2+9\,y^2+16\,z^2+12\,xy-24yz-16xz }$

$\textbf{Solution:}$

$\text{Consider,}$

$4\,x^2+9\,y^2+16\,z^2+12\,xy-24yz-16xz$

$=(2x)^2+(3y)^2+(-4z)^2+2\,(2x)(3y)+2(3y)(-4z)+2(2x)(-4z)$

$\text{Using the algebraic identity,}$

$\boxed{\bf\,(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca}$ $\text{we get}$

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

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

$\therefore\bf\,4\,x^2+9\,y^2+16\,z^2+12\,xy-24yz-16xz=(2x+3y-4z)^2$

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Answer 2

Answer:

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