Question

Expand (-4x+2y-z)^2 using suitable identity

Answer 1

Answer:

$16x^2+4y^2+z^2-8xy-4yz+8zx$

The most suitable identity to expand the given expression is : ↓↓↓

$(A+B+C)^2=A^2+B^2+C^2+2AB+2BC+2CA$.

Subtract $A=-4x$, $B=2y$ and $C=-z$.

∴ $(-4x+2y-z)^2=16x^2+4y^2+z^2-8xy-4yz+8zx$

( tip : That $(-4x+2y-z)^2= (4x-2y+z)^2$ can be used. )