Prove that 0⋅a=00 \cdot a = 00⋅a=0 for any real number aaa. Which step uses the distributive axiom?
a+a=aa + a = aa+a=a (additive identity)
0⋅a=(0+0)a=0⋅a+0⋅a0 \cdot a = (0 + 0)a = 0 \cdot a + 0 \cdot a0⋅a=(0+0)a=0⋅a+0⋅a
0⋅a=1⋅a−1⋅a0 \cdot a = 1 \cdot a - 1 \cdot a0⋅a=1⋅a−1⋅a
0+0=00 + 0 = 00+0=0 (additive identity)