Question

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

Answer 1

Step-by-step explanation:

• Use Cube of Difference: $\tt {(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}$

.

$\tt \implies(5p-3q)({(5p)}^{2}-2\times 5p\times 3q+{(3q)}^{2})$

$\tt\implies (5p-3q)(25{p}^{2}-30pq+9{q}^{2})$

• Expand by distributing sum groups.

$\tt \implies5p(25{p}^{2}-30pq+9{q}^{2})-3q(25{p}^{2}-30pq+9{q}^{2})$

• Expand by distributing terms.

$\tt\implies 125{p}^{3}-150{p}^{2}q+45p{q}^{2}-(75q{p}^{2}-90{q}^{2}p+27{q}^{3})$

• Remove parentheses.

$\tt\implies 125{p}^{3}-150{p}^{2}q+45p{q}^{2}-75q{p}^{2}+90{q}^{2}p-27{q}^{3}$

• Collect like terms.

$\tt\implies 125{p}^{3}+(-150{p}^{2}q-75{p}^{2}q)+(45p{q}^{2}+90p{q}^{2})-27{q}^{3}$

• Simplify.

$\tt\implies 125{p}^{3}-225{p}^{2}q+135p{q}^{2}-27{q}^{3}$