Question

Expand the following:
(2р – Зq)³​

Answer 1

Answer:

Question :-

Expand the following:

(2р – Зq )³

Required Answer :-

${8p}^{3} -18 {p}^{2} q + 18p {q}^{2} - {27q}^{3}$

Solution :-

Formula used here :-

${(a - b)}^{3} = {a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - {b}^{3}$

Now let's substitute given values in place of a and b

${(2p - 3p)}^{3} = {2p}^{3} - 3 \times {2p}^{2} \times 3q + 3 \times 2p \times {3q}^{2} - {3q}^{3}$

$= {8p}^{3} - 18 {p}^{2} q + 18p {q}^{2} - {27q}^{3}$

Therefore the answer is 8p³-18p²q+18pq²-27³

Answer 2

Question :-

Expand the following:

(2р – Зq )³

Required Answer :-

{8p}^{3} -18 {p}^{2} q + 18p {q}^{2} - {27q}^{3}8p

3

−18p

2

q+18pq

2

−27q

3

Solution :-

Formula used here :-

{(a - b)}^{3} = {a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - {b}^{3}(a−b)

3

=a

3

−3a

2

b+3ab

2

−b

3

Now let's substitute given values in place of a and b

{(2p - 3p)}^{3} = {2p}^{3} - 3 \times {2p}^{2} \times 3q + 3 \times 2p \times {3q}^{2} - {3q}^{3}(2p−3p)

3

=2p

3

−3×2p

2

×3q+3×2p×3q

2

−3q

3

= {8p}^{3} - 18 {p}^{2} q + 18p {q}^{2} - {27q}^{3}=8p

3

−18p

2

q+18pq

2

−27q

3

Therefore the answer is 8p³-18p²q+18pq²-27