Question

: Write the following cubes in the expanded form:
(i) (3a + 4b)
(ii) (5p - 39)
13 3
a
find

Answer 1

Answer:

(A) The given statement is:]

(3a+4b)^3(3a+4b)3

Using the identity (a+b)^3=a^3+b^3+3a^2b+3ab^2(a+b)3=a3+b3+3a2b+3ab2 , we have

=(3a)^3+(4b)^3+3(3a)^2(4b)+3(3a)(4b)^2(3a)3+(4b)3+3(3a)2(4b)+3(3a)(4b)2

=27a^3+64b^3+108a^2b+144ab^227a3+64b3+108a2b+144ab2

which is the required expanded form.

(B) The given statement is:

(5p-3q)^3(5p−3q)3

Using the identity (a-b)^3=a^3-b^3-3a^2b+3ab^2(a−b)3=a3−b3−3a2b+3ab2 , we have

=(5p)^3-(3q)^3-3(5p)^2(3q)+3(5p)(3q)^2(5p)3−(3q)3−3(5p)2(3q)+3(5p)(3q)2

=125p^3-27q^3-225p^2q+135pq^2125p3−27q3−225p2q+135pq2

which is the required expanded form