Coefficient of [tex]x^2y^2[/tex] = 24
Solution:
Given that:
[tex](2x - y)^4[/tex]
We have to find the coefficient of [tex]x^2y^2[/tex] term
Use the following algebraic formula
[tex](a-b)^4 = a^4 - 4a^3b+6a^2b^2-4ab^3+b^4[/tex]
From given,
[tex](2x - y)^4[/tex]
Where,
a = 2x
b = y
Therefore, by using formula, we get,
[tex](2x - y)^4 = (2x)^4 - 4(2x)^3(y) + 6(2x)^2(y)^2 - 4(2x)(y)^3 + y^4\\\\Simplify\\\\(2x - y)^4 = 16x^4 - 32x^3y + 24x^2y^2-8xy^3 + y^4[/tex]
Find the coefficient of [tex]x^2y^2[/tex]
From above simplified expression,
coefficient of [tex]x^2y^2[/tex] = 24
