Without expanding the following determinant, show that : `|[[3p+q, 2p, p],[4p+3q, 3p, 3p],[5p+6q,4p,6p]]|=p^3`

Show that: |[p-q-r,2p,2p],[2q,q-r-p,2q],[2r,2r,r-p-q]|=(p+q+r)^3

Using the properties of determinants show that : |[[p^2, q^2, r^2],[qr,rp,pq],[p,q,r]]|=(p-q)(q-r)(r-p)(pq+qr+rp)

Solve the following equations: (3p)/4 = 6

Prove that: |[1,1+p,1+p+q],[2,3+2p,4+3p+2q],[3,6+3p,10+6p+3q]|=1

Using the properties of determinant, show that : |[1,p+q,p^2+q^2],[1,q+r,q^2+r^2],[1,r+p,r^2+p^2]| = (p-q)(q-r)(r-p)

Write the following cube in the expanded form: (5p -3q)^3

Factorize the following expressions (p+q)^3-p-q

Find the product of the following pairs of monomials: 4p^3 , – 3p

Find the following squares by using the identities. (4p-3q)^2