LetKbe a field, charK≠2, and letVkbe ak-dimensional vector space overKequipped with a nondegenerate symmetric bilinear form. DenoteCkthe Clifford algebra ofVk. We study the polynomial identities for the pair (Ck,Vk). A basis of the identities for this pair is found. It is proved that they are consequences of the single identity [x2,y] = 0 whenk= ∝ It is shown that whenk< ∝ the identities for (Ck,Vk) follow from[x2,y]=0 andWk+1= 0 whereWk+1is an analog of the standard polynomialStk+1DenoteM2(K) the matrix algebra of order two overK, and letsl2(K) be the Lie algebra of all traceless 2 × 2 matrices overK. As an application, new proof of the fact that the identity [x2,y] = 0 is a basis of the weak Lie identities for the pair (M2(K),sl2(K) is given.