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