Question

The coefficient of x2y in the expansion of (4x+5y)3 is equal to

Answer 1

The coefficient of $x^2y$ in the expansion of $(4x+5y)^3$ is equal to 240.

Step-by-step explanation:

We have,

$(4x+5y)^3$

To find, the coefficient of $x^2y$ in the expansion of $(4x+5y)^3$ = ?

Using the algebraic identity,

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

∴ $(4x+5y)^3$

Here, a = 4x and b = 5y

$(4x+5y)^3$$=(4x)^{3}+3(4x)^{2}(5y)+3(4x)(5y)^{2}+(5y)^{3}$

$=64x^{3}+15y.16x^{2}+12x.25y^{2}+125y^{3}$

$=64x^{3}+240x^{2}y+300xy^{2}+125y^{3}$

$=(64)x^{3}+(240)x^{2}y+(300)xy^{2}+(125)y^{3}$

Clearly, the coefficient of $x^2y$ in the expansion of $(4x+5y)^3$ = 240

Thus, the coefficient of $x^2y$ in the expansion of $(4x+5y)^3$ is equal to 240.