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From expansion of solids we know that 
v = v₀(1+γt)                             .....1
here v = final volume 
       v₀ = initial volume
       γ = co-efficient of volume expansion
       t = tempareture difference
as the mass(m) remains same during expansion so we can write from equation 1
m/v = m/{v₀(1+γt)}
⇒m/v = m/v₀ × 1/(1+γt)
⇒ρ = ρ₀ × (1+γt)⁻¹ (ρ = density)
⇒ρ = ρ₀(1-γt)

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