One method is:
$$8p^3-27q^3$$
Rewrite the expression as the difference of perfect cubes:
$$\left({{\mathtt{2}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{p}}}^{{\mathtt{3}}}\right){\mathtt{\,-\,}}\left({{\mathtt{3}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{q}}}^{{\mathtt{3}}}\right)$$
Disregard the () and the cubes to see; 2p-3q
Using 2p-3q, square the first term to get 4p2, multiply the two terms to get 6pq (disregard the minus sign), square the last term to get 9q2.
The result should be (2p-3q)(4p2+6pq+9q2)
One method is:
$$8p^3-27q^3$$
Rewrite the expression as the difference of perfect cubes:
$$\left({{\mathtt{2}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{p}}}^{{\mathtt{3}}}\right){\mathtt{\,-\,}}\left({{\mathtt{3}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{q}}}^{{\mathtt{3}}}\right)$$
Disregard the () and the cubes to see; 2p-3q
Using 2p-3q, square the first term to get 4p2, multiply the two terms to get 6pq (disregard the minus sign), square the last term to get 9q2.
The result should be (2p-3q)(4p2+6pq+9q2)
