Question

Find the cube of $a+3b$.

• A. $a^3+27b^3+9a^{2}b+27a{b}^2$
• B. $125a^3-27b^3-225a^{2}b-135a{b}^2$
• C. $a^3+27b^3+225a^{2}b+135a{b}^2$
• D. $a^3+b^3+9a^{2}b+27a{b}^2$

Answer 1

The correct option is A $a^3+27b^3+9a^{2}b+27a{b}^2$

Using the identity,

$(a+b{)}^3=a^3+b^3+3ab(a+b)$,

$(a+3b{)}^3$

= $(a{)}^3+(3b{)}^3+3\times a\times 3b(a+3b)$

= $a^3+27b^3+9ab(a+3b)$

= $a^3+27b^3+9a^{2}b+27a{b}^2$