Question

Write the following cubes in the expanded form:

(i) (3a + 4b)3

(ii) (5p – 3q)3

Answer 1

Answer:

Step-by-step explanation:

(A) The given statement is:]

$(3a+4b)^3$

Using the identity $(a+b)^3=a^3+b^3+3a^2b+3ab^2$, we have

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

=$27a^3+64b^3+108a^2b+144ab^2$

which is the required expanded form.

(B) The given statement is:

$(5p-3q)^3$

Using the identity $(a-b)^3=a^3-b^3-3a^2b+3ab^2$, we have

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

=$125p^3-27q^3-225p^2q+135pq^2$

which is the required expanded form.

Answer 2

Answer:

$i) Expansion \: of \:(3a+4b)^{3}\\=27a^{3}+108a^{2}b+192ab^{2}+64b^{3}$

$ii) Expansion \:of\:(5p-3q)^{3}\\=125p^{3}-150p^{2}q+135pq^{2}-27q^{3}$

Step-by-step explanation:

$i) Expansion \: of \:(3a+4b)^{3}\\=(3a)^{3}+3\times (3a)^{2}\times 4b+3\times 3a\times (4b)^{2}+(4b)^{3}$

/* By algebraic identity:

(a+b)³ = a³+3a²b+3ab²+b³ */

$=27a^{3}+108a^{2}b+192ab^{2}+64b^{3}$

$ii) Expansion \:of\:(5p-3q)^{3}\\=(5p)^{3}-3\times (5p)^{2}\times 3p+3\times 5p\times (3q)^{2}-(3q)^{3}$

/* By algebraic identity:

(a-b)³ = a³-3a²b+3ab²-b³ */

$=125p^{3}-150p^{2}q+135pq^{2}-27q^{3}$

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