The coefficient of x^{3} y in (x-2 y) \times (5 x+y)^{3} is

SSC CHSL 5 Aug 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 66 of 100

Marks: +1, -0

The coefficient of

x^{3} y

(x-2 y) ×

(5 x+y)^{3}

Solution:

(x-2 y)(5 x+y)^{3}

=(x-2 y)

[(5 x)^{3}+(y)^{3}+3 × 5 x × y ×(5 x+y)]

=(x-2 y)

[125 x^{3}+y^{3}+15 x y ×(5 x+y)]

=(x-2 y)

(125 x^{3}+y^{3}+75 x^{2} y+15 x y^{2})

=125 x^{4}+x y^{3}+75 x^{3} y+15 x^{2} y^{2}

-250 x^{3} y-2 y^{4}-150 x^{2} y^{2}-30 x y^{3}

∴

Coefficient of

x^{3} y=-250+75

=-175

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