Question

The value of $(2x+3y{)}^3$ is __________.

• A. $8x^3+27y^3+36x^{2}y+54x{y}^2$
• B. $8x^3-27y^2-36x^{2}y+54x{y}^2$
• C. $8x^3+36y^3+36x^{2}y+54x{y}^2$
• D. $18x^3+27y^3+36x^{2}y+54x{y}^2$

Answer 1

The correct option is A

$8x^3+27y^3+36x^{2}y+54x{y}^2$

We know the identity,
$(a+b{)}^3=a^3+b^3+3a^{2}b+3a{b}^2$

$(2x+3y{)}^3=(2x{)}^3+(3y{)}^3+3(2x{)}^2\times \left(3y\right)+3\times \left(2x\right)\times (3y{)}^2$

= $8x^3+27y^3+36x^{2}y+54x{y}^2$