Question

Find the cube of 5a+3b .

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

Answer 1

The correct option is B $125a^3+27b^3+225a^{2}b+135a{b}^2$

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

$(5a+3b{)}^3=(5a{)}^3+(3b{)}^3+3\times 5a\times 3b(5a+3b)$

= $125a^3+27b^3+45ab(5a+3b)$

= $125a^3+27b^3+225a^{2}b+135a{b}^2$