Question

3. Write the following cubes in the expanded form:
(ii) (5p – 3q)3

Answer 1

Given,

• (5p-3q)³ is given.

To find,

• We have to expand (5p-3q)³.

Solution,

We can simply expand (5p-3q)³ by using the following cubic identity:

                (a-b)³ = a³-b³-3ab(a-b)     (*)

Now, using (*), we have a = 5p and b = 3q

               (5p-3q)³ = (5p)³ -(3q)³-3(5p)(3q)[5p-3q]

                             = 125p³ -27q³-45pq(5p-3q]

                             = 125p³-27q³-225p²q+135pq²

Hence, the cube (5p-3q)³ in the expanded form is 125p³-27q³-225p²q+135pq².

Answer 2

Answer:

Given,

• (5p-3q)³ is given.

To find,

We have to expand (5p-3q)³.

Solution,

We can simply expand (5p-3q)³ by using the following cubic identity:

(a-b)3 = a³-b³-3ab(a-b) (*)

=3q Now, using (*), we have a = 5p and b = (5p-3q)3 = (5p)³ -(3q)³-3(5p)(3q)

[5p-3q]

= 125p3

-27q3-45pq(5p-3q]

=

125p³-27q*-225p²q+135pq²

Hence, the cube (5p-3q)³ in the expanded form is 125p³-27q³-225p²q+135pq².