Question
Write the following in the expanded form:
$(-2 x+3 y+2 z)^2$
$(-2 x+3 y+2 z)^2$
✓
Answer
We have,
$(-2 x+3 y+2 z)^2$
$=(-2 x)^2+(3 y)^2+(2 z)^2+2(-2 x)(3 y)+2(3 y)(2 z)+2(-2 x)(2 z)$
${\left[\therefore(x+y+z)^2=x^2+y^2+z^2+2 x y+2 y z+2 x z\right]}$
$(-4 x+6 y+4 z)^2$
$=4 x^2+9 y^2+4 z^2-12 x y+12 y z-8 x z$
$(-2 x+3 y+2 z)^2$
$=(-2 x)^2+(3 y)^2+(2 z)^2+2(-2 x)(3 y)+2(3 y)(2 z)+2(-2 x)(2 z)$
${\left[\therefore(x+y+z)^2=x^2+y^2+z^2+2 x y+2 y z+2 x z\right]}$
$(-4 x+6 y+4 z)^2$
$=4 x^2+9 y^2+4 z^2-12 x y+12 y z-8 x z$
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